Algebra and Trigonometry: Real Mathematics, Real People (7th Edition)
Verified Answer ✓
: ; : units; : units ; The sum of all the angles... more
Verified Answer ✓
: ; : feet ; Find the angle after tilting the ... more
Verified Answer ✓
: ; : ;: unit ; Draw the triangle with given sides... more
Verified Answer ✓
Entire Proof Answer:Use the Law of Sines in ... more
Verified Answer ✓
; ; ; ; ; Use the formula to find the height ... more
Verified Answer ✓
square meters ; Draw the triangle with given ... more
Verified Answer ✓
; Consider triangle ABC has sides a, b, c, and ... more
Verified Answer ✓
Oblique ; An oblique triangle is a triangle that ... more
Verified Answer ✓
; The rule is called the sine rule. Here the ... more
Verified Answer ✓
; The formulae , and are used to determine the ... more
Verified Answer ✓
Angles ; Any triangle with two angles and one side... more
Verified Answer ✓
The two cases given are two angles and one side, ... more
Verified Answer ✓
Yes, it is always true that the longest side of a ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; Use the law of sines in a reciprocal form to ... more
Verified Answer ✓
; Use the law of sine in reciprocal form to find... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; Use the law of sine in reciprocal form to find ... more
Verified Answer ✓
; Use the law of sine in reciprocal form to find ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; The sum of all the angles in a triangle is . ... more
Verified Answer ✓
; Use the law of sine in reciprocal form to find... more
Verified Answer ✓
; Use the law of sine in reciprocal form to find... more
Verified Answer ✓
No solution ; Use the law of sine in reciprocal ... more
Verified Answer ✓
No solution ; In any triangle, the greatest angle ... more
Verified Answer ✓
No solution ; In any triangle, the greatest angle ... more
Verified Answer ✓
,when , when ; In the given triangle one angle is ... more
Verified Answer ✓
,when , when ; It is given one angle is acute, , ... more
Verified Answer ✓
No solution ; Consider the sides and angle for a ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
; Use the formula of area for an oblique triangle... more
Verified Answer ✓
; The area of any triangle is one-half of the ... more
Verified Answer ✓
; The area of any triangle is one-half of the ... more
Verified Answer ✓
; The area of any triangle is one-half of the ... more
Verified Answer ✓
; The area of any triangle is one-half of the ... more
Verified Answer ✓
; The area of any triangle is one-half of the ... more
Verified Answer ✓
24.12 meters ; Sketch the visual diagram of the ... more
Verified Answer ✓
77 meters ; Sketch the visual diagram of the given... more
Verified Answer ✓
; Sketch the visual diagram of the given problem... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
: ; : ; Redraw the diagram given in the problem. ... more
Verified Answer ✓
; Refer to the given diagram and substitute 17 ... more
Verified Answer ✓
; Redraw the given visual representation of the ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
False, there is a need of at least one angle when ... more
Verified Answer ✓
True, as one of the angle is more than , the other... more
Verified Answer ✓
False, for a unique solution the condition must ... more
Verified Answer ✓
YesSince two angles are given, use the triangle ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
; Use the quotient property of Tangent function ... more
Verified Answer ✓
; Use the reciprocal property of Cotangent ... more
Verified Answer ✓
; Write the given expression as the sum or ... more
Verified Answer ✓
; Write the given expression as the sum or ... more
Verified Answer ✓
; Write the given expression as the sum or ... more
Verified Answer ✓
; Write the given expression as the sum or ... more
Verified Answer ✓
Pythagoras theoremThe Pythagoras theorem is a ... more
Verified Answer ✓
On solving side , any of the angle or can be ... more
Verified Answer ✓
Yes, the given formulas can be used to find the ... more
Verified Answer ✓
; The values of the sides of the triangle are... more
Verified Answer ✓
; The values of the sides of the triangle are , ... more
Verified Answer ✓
feet ; Plot the figure for the given information.... more
Verified Answer ✓
; Substitute 30 for , 56 for , and 40 for into ... more
Verified Answer ✓
19.90 square feet ; Use Heron’s formula to ... more
Verified Answer ✓
; For a triangle with angles A, B, and C, ... more
Verified Answer ✓
; The area of a triangle, right-angled at C, with... more
Verified Answer ✓
No ; The ASA, that is, two angles and included ... more
Verified Answer ✓
Yes ; The SAS, that is, two sides and their ... more
Verified Answer ✓
Yes ; The SSS, that is, three sides of the ... more
Verified Answer ✓
No ; The SSA, that is, two sides and an angle ... more
Verified Answer ✓
; The values of the sides of the triangle are... more
Verified Answer ✓
; The values of the sides of the triangle are... more
Verified Answer ✓
; The values of the sides of the triangle are , ... more
Verified Answer ✓
; The values of the sides of the triangle are... more
Verified Answer ✓
; The values of the sides of the triangle are , ... more
Verified Answer ✓
; The values of the sides of the triangle are , ... more
Verified Answer ✓
; The values of the sides of the triangle are... more
Verified Answer ✓
; The values of the sides of the triangle are... more
Verified Answer ✓
; The values of the sides of the triangle are , ... more
Verified Answer ✓
; The values of the sides of the triangle are , ... more
Verified Answer ✓
; The values of the sides of the triangle are , ... more
Verified Answer ✓
; The values of the sides of the triangle are , ... more
Verified Answer ✓
; The values of the sides of the triangle are... more
Verified Answer ✓
; The values of the sides of the triangle are... more
Verified Answer ✓
; The values of the sides of the triangle are... more
Verified Answer ✓
; The values of the sides of the triangle are , ... more
Verified Answer ✓
; The sides of the triangle are and . The given ... more
Verified Answer ✓
; The sides of the triangle are and . The given ... more
Verified Answer ✓
48 ; From the given table,the values of sides a, ... more
Verified Answer ✓
2535 ; From the given table,The values of sides a... more
Verified Answer ✓
101420 ; From the given table,The values of sides... more
Verified Answer ✓
406080 ; From the given table,The values of sides... more
Verified Answer ✓
; Plot the figure for the given information.Apply... more
Verified Answer ✓
; Plot the figure for the given information.Apply... more
Verified Answer ✓
Law of Cosines ; From the given triangle ABC, the ... more
Verified Answer ✓
Law of Sine ; From the given triangle ABC, the ... more
Verified Answer ✓
Law of Cosines ; The values of sides a, c, and ... more
Verified Answer ✓
Law of Cosines ; The values of sides a, b, and ... more
Verified Answer ✓
Law of SineNo triangle will be formed ; The values... more
Verified Answer ✓
Law of Cosines ; The values of sides a, b, and c ... more
Verified Answer ✓
Law of Sine ; The values of side c and the angles ... more
Verified Answer ✓
Law of Sine ; The values of sides b, c, and angle ... more
Verified Answer ✓
104.57 square units ; Use Heron’s formula to ... more
Verified Answer ✓
385.70 square units ; Use Heron's formula to ... more
Verified Answer ✓
19.81 square units ; Use Heron’s formula to ... more
Verified Answer ✓
43.52 square units ; Use Heron’s formula to ... more
Verified Answer ✓
0.27 square units ; Use Heron’s formula to ... more
Verified Answer ✓
2.57 square units ; Use Heron’s formula to ... more
Verified Answer ✓
0.18 square units ; Use Heron’s formula to ... more
Verified Answer ✓
0.11 square units ; Use Heron’s formula to ... more
Verified Answer ✓
483.40 meters ; Refer to the given figure.Assume ... more
Verified Answer ✓
; Refer to the given figure.Substitute 2 for a , ... more
Verified Answer ✓
Verified Answer ✓
miles ; Assume that the ship that leaves the port ... more
Verified Answer ✓
Approx ; The length of the sides a,b, and c of the... more
Verified Answer ✓
feet5 feetfeet ; Substitute the value of height (h... more
Verified Answer ✓
feetfeet ; The sidehill angle of the tower is . As... more
Verified Answer ✓
feet ; Draw the figure by using the given ... more
Verified Answer ✓
Approx ; The length of the sides a,b, and c of the... more
Verified Answer ✓
Approx ; Compute the height of the parallelogram ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
True The Law of cosines is used to find the side ... more
Verified Answer ✓
False ; The area of a triangle with sides of ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Result obtained from both the methods is the same.... more
Verified Answer ✓
Verified Answer ✓
; Since function has an inverse in the interval... more
Verified Answer ✓
; Since function has an inverse in the interval... more
Verified Answer ✓
; Since function has an inverse in the interval... more
Verified Answer ✓
; Since function has an inverse in the interval... more
Verified Answer ✓
Equivalent Vectors ; Calculate the magnitude of ... more
Verified Answer ✓
; Consider the given points and ; vector can be... more
Verified Answer ✓
Verified Answer ✓
; Divide by its magnitude to calculate the unit ... more
Verified Answer ✓
; Calculate the vector using vector component ... more
Verified Answer ✓
; Substitute the value of vectors and and ... more
Verified Answer ✓
Verified Answer ✓
; As the plane is descending at an angle of with... more
Verified Answer ✓
2,405 pounds ; Let be the combined weight of the ... more
Verified Answer ✓
miles per hour; ; Draw the figure with the help of... more
Verified Answer ✓
Directed line segment ; Any quantity that requires... more
Verified Answer ✓
InitialTerminal ; The directed line segment will ... more
Verified Answer ✓
Magnitude ; If and are two vectors .The ... more
Verified Answer ✓
Vector ; Two lines are equivalent to each other if... more
Verified Answer ✓
Standard position ; A vector is the collection of... more
Verified Answer ✓
Multiplication ; Scalar multiplication and vector ... more
Verified Answer ✓
Resultant ; The result obtained by adding two ... more
Verified Answer ✓
Linear combinationHorizontalVertical ; can be ... more
Verified Answer ✓
Magnitude and direction ; Two directed line ... more
Verified Answer ✓
Unit vector ; Any vector that has magnitude equal ... more
Verified Answer ✓
Entire proof Answer: Represent and in component ... more
Verified Answer ✓
Entire proof Answer: Represent and in component ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
; Consider the given points and . Vector is ... more
Verified Answer ✓
T product of the vector, and scalar is a vector ... more
Verified Answer ✓
T product of the vector and scalar three is a ... more
Verified Answer ✓
To add the vectors and , position them so that ... more
Verified Answer ✓
The vector, will have a direction directly ... more
Verified Answer ✓
The vector, will have a direction directly ... more
Verified Answer ✓
The vector, will have the same direction as that ... more
Verified Answer ✓
The magnitude of vector is two times the ... more
Verified Answer ✓
The magnitude of vector is three times the ... more
Verified Answer ✓
Vector have the same direction as that of vector... more
Verified Answer ✓
Vector has the same direction as that of vector ... more
Verified Answer ✓
Vector has the same direction as that of vector ... more
Verified Answer ✓
The vector will have the same direction as that ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
; To find the vector , apply the parallelogram ... more
Verified Answer ✓
; The vector is generated by joining the ... more
Verified Answer ✓
; The vector is generated by joining the ... more
Verified Answer ✓
; The vector is generated by joining the ... more
Verified Answer ✓
; In order to find the unit vector in the ... more
Verified Answer ✓
; In order to find the unit vector in the ... more
Verified Answer ✓
; In order to find the unit vector in the ... more
Verified Answer ✓
; In order to find the unit vector in the ... more
Verified Answer ✓
; In order to find the unit vector in the ... more
Verified Answer ✓
; In order to find the unit vector in the ... more
Verified Answer ✓
; In order to find the unit vector in the ... more
Verified Answer ✓
; In order to find the unit vector in the ... more
Verified Answer ✓
; Divide vector by its magnitude to find the ... more
Verified Answer ✓
; Divide vector by its magnitude to find the ... more
Verified Answer ✓
; Divide vector by its magnitude to find the ... more
Verified Answer ✓
; Divide vector by its magnitude to find the ... more
Verified Answer ✓
; Divide vector by its magnitude to find the ... more
Verified Answer ✓
; Divide vector by its magnitude to find the ... more
Verified Answer ✓
; Divide vector by its magnitude to find the ... more
Verified Answer ✓
; Divide vector by its magnitude to find the ... more
Verified Answer ✓
; Subtract initial point from terminal point to ... more
Verified Answer ✓
; Subtract initial point from terminal point to ... more
Verified Answer ✓
; Subtract initial point from terminal point to ... more
Verified Answer ✓
; Subtract initial point from terminal point to ... more
Verified Answer ✓
; In order to find the component form of vector... more
Verified Answer ✓
; In order to find the component form of vector... more
Verified Answer ✓
; Substitute the value of vector and in and ... more
Verified Answer ✓
; Substitute vectors and in vector . ; Add ... more
Verified Answer ✓
; Substitute vectors and in given vector. ; Add... more
Verified Answer ✓
; Substitute vectors and in given vector. ; Add... more
Verified Answer ✓
; Substitute the values of and . ; ; Calculate... more
Verified Answer ✓
; Substitute the values of and . ; Calculate the... more
Verified Answer ✓
; Compute the magnitude of the given vector. ; ... more
Verified Answer ✓
; Evaluate the magnitude of the given vector. ; ... more
Verified Answer ✓
; Calculate the magnitude of the given vector. ; ... more
Verified Answer ✓
; Calculate the magnitude of the given vector. ; ... more
Verified Answer ✓
; Components of vector having is calculated as, ... more
Verified Answer ✓
; Components of vector having is calculated as,... more
Verified Answer ✓
; Components of vector having is calculated as,... more
Verified Answer ✓
; As components of vector is calculated as, ... more
Verified Answer ✓
; As , components of vector is calculated as,... more
Verified Answer ✓
; Calculate components of vector . ; The ... more
Verified Answer ✓
; As vector is in direction of , find the unit ... more
Verified Answer ✓
; As vector is in the direction of , find the ... more
Verified Answer ✓
; Find the components of vector and . ; ; ... more
Verified Answer ✓
; Find the components of vector and . ; Write ... more
Verified Answer ✓
; Calculate the components of vector and . ; ... more
Verified Answer ✓
; Calculate the components of vector and... more
Verified Answer ✓
Approx ; Assume Force1() is along x-axis and ... more
Verified Answer ✓
; Find the vector using the vectors given. ; ... more
Verified Answer ✓
; Write the given vectors in terms of the angle ... more
Verified Answer ✓
; Write the given vectors in terms of the angle ... more
Verified Answer ✓
; The force 1 is along the positive -axis and ... more
Verified Answer ✓
; Assume Force1() is along x-axis and Force2() is... more
Verified Answer ✓
Approx Approx ; Let the horizontal component be ... more
Verified Answer ✓
Approx Approx ; Let the horizontal component be ... more
Verified Answer ✓
poundspounds ; Draw the free body diagram ... more
Verified Answer ✓
Approx poundsApprox pounds ; Draw the free body ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
km/hr; ; Draw a free body diagram of airplane ... more
Verified Answer ✓
Verified Answer ✓
TrueAs a vector has only two components, magnitude... more
Verified Answer ✓
TrueRearranging the equation of unit vector in ... more
Verified Answer ✓
TrueAs each component is zero, equating the sum of... more
Verified Answer ✓
TrueEquating the magnitude of vector with unity ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Entire Proof Answer: Consider the scalars, as the... more
Verified Answer ✓
Follow the listed steps to perform vector ... more
Verified Answer ✓
:;: ; In reference to the graph given in the ... more
Verified Answer ✓
: ; : ; In reference to the graph given in the ... more
Verified Answer ✓
Verified Answer ✓
; Using the rules of addition and subtraction of ... more
Verified Answer ✓
; Use the rules of addition and subtraction of ... more
Verified Answer ✓
, ; Simplify the given expression by using the ... more
Verified Answer ✓
, ; Simplify the given expression by using the ... more
Verified Answer ✓
; Group decimal numbers and power terms with base... more
Verified Answer ✓
; Group decimal numbers and power terms with base... more
Verified Answer ✓
; Equate to zero to solve for . ; ; Take on ... more
Verified Answer ✓
; Equate to zero to solve for . ; Take on both ... more
Verified Answer ✓
; Subtract 4 from both sides in the given ... more
Verified Answer ✓
; Subtract 18 from both sides in the given ... more
Verified Answer ✓
; Substitute for in the given expression. ; Use... more
Verified Answer ✓
; Substitute for in the given expression. ; ... more
Verified Answer ✓
; Write the dot product of the given vectors and... more
Verified Answer ✓
Verified Answer ✓
; Find the dot product of the vectors and . ; ... more
Verified Answer ✓
Orthogonal ; Two vectors are orthogonal when their... more
Verified Answer ✓
; Calculate the dot product of and . ; Calculate... more
Verified Answer ✓
pounds ; Write the gravitational force that acts ... more
Verified Answer ✓
foot-pounds ; Let be the force applied on the ... more
Verified Answer ✓
Yes ; Dot products are distributive in nature.... more
Verified Answer ✓
0 ; The dot product of two vectors is given as .... more
Verified Answer ✓
Scalar ; In the dot product of vectors, the ... more
Verified Answer ✓
; The dot product of two vectors is given as . ... more
Verified Answer ✓
; Let be a vector whose projection onto is . ... more
Verified Answer ✓
or ; Work done by a constant force , as its point ... more
Verified Answer ✓
0 ; Apply the formula of dot product and simplify... more
Verified Answer ✓
; Write the dot product of the given vectors and... more
Verified Answer ✓
14 ; Write the given vectors and in component ... more
Verified Answer ✓
36 ; Write and in component form. ; Substitute ... more
Verified Answer ✓
8Scalar ; Calculate the dot product of with ... more
Verified Answer ✓
Scalar ; Calculate the dot product of and . ; ... more
Verified Answer ✓
Scalar ; Calculate the vector . ; Calculate the ... more
Verified Answer ✓
Scalar ; Calculate the dot product of and . ; The... more
Verified Answer ✓
; Vector ; Multiply by 3 to find . ; ; Use the... more
Verified Answer ✓
Vector ; Multiply by 2 to find . ; Use the ... more
Verified Answer ✓
13 ; Use the formula to calculate the magnitude ... more
Verified Answer ✓
17 ; Use the formula to calculate the magnitude ... more
Verified Answer ✓
; Use the formula to calculate the magnitude of... more
Verified Answer ✓
; Write in terms of its components. ; Use the ... more
Verified Answer ✓
4 ; Write in terms of its components. ; Use the ... more
Verified Answer ✓
9 ; Write in terms of its components. ; Use the ... more
Verified Answer ✓
; Find the dot product of the vectors and . ; ... more
Verified Answer ✓
; Find the dot product of the vectors and . ; ... more
Verified Answer ✓
; Write the given vectors and in component form... more
Verified Answer ✓
; Write the given vectors and in terms of its ... more
Verified Answer ✓
; Write the given vectors and in terms of its ... more
Verified Answer ✓
; Write the given vectors and in terms of its ... more
Verified Answer ✓
; Substitute the values of ,,, and into the ... more
Verified Answer ✓
; Substitute the values of , , , and into the ... more
Verified Answer ✓
; Sketch the graph of the given vectors and in ... more
Verified Answer ✓
; Sketch the graph of the given vectors and in ... more
Verified Answer ✓
; Sketch the graph of the given vectors and in ... more
Verified Answer ✓
; Sketch the graph of the given vectors and in ... more
Verified Answer ✓
; ; ; Let , , and, , write these in terms of three... more
Verified Answer ✓
; ; ; Let , , and, , write these in terms of ... more
Verified Answer ✓
;; ; Let , , and, , write these in terms of three... more
Verified Answer ✓
;; ; Let , , and .Write the vertices , , and of ... more
Verified Answer ✓
; Substitute the given magnitudes of and and ... more
Verified Answer ✓
24 ; Substitute the given magnitudes of and and ... more
Verified Answer ✓
; Substitute the given magnitudes of and and ... more
Verified Answer ✓
; To find the dot product , rewrite the formula ... more
Verified Answer ✓
and are orthogonal. ; Calculate the dot product ... more
Verified Answer ✓
and are not orthogonal. ; If the dot product of ... more
Verified Answer ✓
and are not orthogonal. ; Write the horizontal ... more
Verified Answer ✓
and are orthogonal. ; Write the horizontal and ... more
Verified Answer ✓
Calculate the dot product of and .The dot product... more
Verified Answer ✓
Calculate the dot product of and .The dot product... more
Verified Answer ✓
Calculate the dot product of and .The dot product... more
Verified Answer ✓
Calculate the dot product of and .The dot product... more
Verified Answer ✓
; Calculate the dot product of vectors, and... more
Verified Answer ✓
; Obtain the dot product of vectors, and . ; The... more
Verified Answer ✓
; Calculate the dot product of vectors, and . ; ... more
Verified Answer ✓
; Calculate the dot product of vectors, and . ; ... more
Verified Answer ✓
; Calculate the dot product of vectors, and . ; ... more
Verified Answer ✓
; Calculate the dot product of vectors, and . ; ... more
Verified Answer ✓
; Calculate the dot product of and . ; Calculate... more
Verified Answer ✓
; Calculate the dot product of and . ; Calculate... more
Verified Answer ✓
; ; Calculate the dot product of and . ; Use the ... more
Verified Answer ✓
; ; Calculate the dot product of and . ; Use the ... more
Verified Answer ✓
; Vectors and are in the same direction, so ... more
Verified Answer ✓
; The given vectors and are parallel to each ... more
Verified Answer ✓
; The vectors and are perpendicular to each ... more
Verified Answer ✓
. ; The vectors and are perpendicular to each ... more
Verified Answer ✓
; ; Let and are the two vectors in opposite ... more
Verified Answer ✓
; ; Let and be two vectors in opposite direction... more
Verified Answer ✓
; ; Let and be two vectors in opposite ... more
Verified Answer ✓
; ; Let and be two vectors in opposite direction... more
Verified Answer ✓
32 ; Calculate the distance vector . ; Apply the ... more
Verified Answer ✓
14 ; Calculate the distance vector . ; The vector... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
5318 pounds ; Write the gravitational force vector... more
Verified Answer ✓
Verified Answer ✓
ft-lb ; The given situation can be represented in ... more
Verified Answer ✓
foot-pounds ; The given situation can be ... more
Verified Answer ✓
foot-pounds ; The given situation can be ... more
Verified Answer ✓
True, The dot product of and is 0. ; Calculate ... more
Verified Answer ✓
False, the work done is a scalar quantity not a ... more
Verified Answer ✓
Orthogonal ; Calculate the dot product of the ... more
Verified Answer ✓
The result of the dot product is a scalar, not a ... more
Verified Answer ✓
; Let the unit vector u be .Calculate .If u is a ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Entire Proof Answer:Let the sides of the rhombus ... more
Verified Answer ✓
Entire Proof Answer: Assume that the vectors and... more
Verified Answer ✓
The vector u is orthogonal to v and w, so the dot ... more
Verified Answer ✓
Draw the unit vector u which makes an angle with ... more
Verified Answer ✓
Draw the unit vector u which makes an angle with ... more
Verified Answer ✓
The function is the horizontal shift of units to... more
Verified Answer ✓
The function is the reflection of with respect ... more
Verified Answer ✓
The function is the upward shift of 6 units of ... more
Verified Answer ✓
The horizontal shrink of the function is . ; Let ... more
Verified Answer ✓
; Apply distributive property to simplify the ... more
Verified Answer ✓
; Apply distributive property to simplify the ... more
Verified Answer ✓
; Apply the identity, to simplify the given ... more
Verified Answer ✓
; Apply the identity, to simplify the given ... more
Verified Answer ✓
; Multiply the numerator and denominator by the ... more
Verified Answer ✓
; Multiply the numerator and denominator by the ... more
Verified Answer ✓
Absolute value: ; The absolute value of any ... more
Verified Answer ✓
; Write the complex number in the form of . ; ... more
Verified Answer ✓
; Find the absolute value of . ; Substitute as ... more
Verified Answer ✓
; The value of is and that of is . Substitute ... more
Verified Answer ✓
; Write the formula of the product of two complex... more
Verified Answer ✓
; Write the formula of the product of two complex... more
Verified Answer ✓
; Write the formula of the division of two ... more
Verified Answer ✓
-4 ; Write the complex number in trigonometric ... more
Verified Answer ✓
; Write the number 1 in trigonometric form by ... more
Verified Answer ✓
; The absolute value of the complex number is... more
Verified Answer ✓
There is a difference between the value of used ... more
Verified Answer ✓
The value of increases in multiples of as the ... more
Verified Answer ✓
; Solve the equation .Write in trigonometric ... more
Verified Answer ✓
Set the value of Tstep as , the resulting graph ... more
Verified Answer ✓
Absolute value ; a in the complex number is ... more
Verified Answer ✓
DeMoivre’s ; DeMoivre’s theorem states that for ... more
Verified Answer ✓
nth root ; A complex number is the nth root of a ... more
Verified Answer ✓
; The complex number is written in the form ... more
Verified Answer ✓
In the trigonometric form , is the distance ... more
Verified Answer ✓
In the trigonometric form , is the angle measured... more
Verified Answer ✓
; Find the absolute value r of the function . ; ... more
Verified Answer ✓
; Find the absolute value r of the function . The... more
Verified Answer ✓
; Find the absolute value r of the function . The... more
Verified Answer ✓
; Find the absolute value r of the function . The... more
Verified Answer ✓
; Find the absolute value r of the function . The... more
Verified Answer ✓
; Find the absolute value r of the function . The... more
Verified Answer ✓
; Find the absolute value r of the function . The... more
Verified Answer ✓
; Find the absolute value r of the function . The... more
Verified Answer ✓
; Write the complex number given as . Find the ... more
Verified Answer ✓
; Look at the graph and write the given complex ... more
Verified Answer ✓
; Look at the graph and get the complex number ... more
Verified Answer ✓
; Look at the graph and get the complex number ... more
Verified Answer ✓
; Look at the graph and get the complex number ... more
Verified Answer ✓
; Look at the graph and get the complex number ... more
Verified Answer ✓
; Look at the graph and get the complex number ... more
Verified Answer ✓
; Look at the graph and get the complex number ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; The complex number is given as . Find the ... more
Verified Answer ✓
; Plot the point on the real axis. ; Compare the... more
Verified Answer ✓
; Plot the point on the real axis. ; Compare the... more
Verified Answer ✓
; To plot the point , move units towards the ... more
Verified Answer ✓
To plot the point , move units towards the ... more
Verified Answer ✓
; To plot the point , move unit towards the ... more
Verified Answer ✓
; To plot the point , move unit towards the ... more
Verified Answer ✓
; To plot the point , move units towards the ... more
Verified Answer ✓
; To plot the point , move units towards the ... more
Verified Answer ✓
; To plot the point , move units towards the ... more
Verified Answer ✓
; To plot the point , move units towards the ... more
Verified Answer ✓
; Substitute the values of and which are and ... more
Verified Answer ✓
; Substitute the value of and in the given ... more
Verified Answer ✓
; Substitute the value of and in the given ... more
Verified Answer ✓
; Substitute the value of and in the given ... more
Verified Answer ✓
; Substitute the value of and in the given ... more
Verified Answer ✓
; Substitute the value of and in the given ... more
Verified Answer ✓
; Use the formula in the given expression and ... more
Verified Answer ✓
; Use the formula in the given expression and ... more
Verified Answer ✓
; Substitute the value of and in the given ... more
Verified Answer ✓
; Substitute the value of and in the given ... more
Verified Answer ✓
; Substitute the value of and which are and ... more
Verified Answer ✓
; Substitute the value of and which are and ... more
Verified Answer ✓
; Enter the expression, into the graphing ... more
Verified Answer ✓
; Enter the expression, into the graphing ... more
Verified Answer ✓
; Enter the expression, into the graphing ... more
Verified Answer ✓
; Enter the expression, into the graphing ... more
Verified Answer ✓
; Suppose and are any complex numbers; then. ... more
Verified Answer ✓
; Suppose and are any complex numbers; then. ... more
Verified Answer ✓
; Suppose and are any complex numbers; then. ... more
Verified Answer ✓
; Suppose and are any complex numbers; then. ... more
Verified Answer ✓
; Suppose and are any complex numbers; then. ... more
Verified Answer ✓
; Suppose and are any complex numbers; then. ... more
Verified Answer ✓
; Suppose and are any complex numbers; then. ... more
Verified Answer ✓
; Suppose and are any complex numbers; then. ... more
Verified Answer ✓
; Suppose and are any general complex numbers; ... more
Verified Answer ✓
; Suppose and are any general complex numbers; ... more
Verified Answer ✓
; Suppose and are any general complex numbers; ... more
Verified Answer ✓
; Suppose and are any general complex numbers; ... more
Verified Answer ✓
; Suppose and are any general complex numbers; ... more
Verified Answer ✓
; Suppose and are any general complex numbers ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
All the powers of lie on the unit circle and ... more
Verified Answer ✓
All the powers of lie on the unit circle and ... more
Verified Answer ✓
Substitute for into the given condition.Use the ... more
Verified Answer ✓
Assume and calculate the modulus. Equate the ... more
Verified Answer ✓
Assume and calculate the modulus. Equate the ... more
Verified Answer ✓
Assume and calculate the modulus. Equate the ... more
Verified Answer ✓
Assume and calculate the modulus. Equate the ... more
Verified Answer ✓
Assume and calculate the modulus. Equate the ... more
Verified Answer ✓
Assume and substitute for , for , and for ... more
Verified Answer ✓
Assume and substitute for , for , and for ... more
Verified Answer ✓
Assume and substitute for , for , and for ... more
Verified Answer ✓
Write an equation using the formula . Since, , ... more
Verified Answer ✓
Write an equation using the argument of the ... more
Verified Answer ✓
Write an equation using the argument of the ... more
Verified Answer ✓
; Since the standard form of a complex number is ... more
Verified Answer ✓
; Since the standard form of a complex number is ... more
Verified Answer ✓
; Since the standard form a complex number is ... more
Verified Answer ✓
; Since the standard form of a complex number is ... more
Verified Answer ✓
; Since the standard form a complex number is ... more
Verified Answer ✓
; Since the standard form of a complex number is ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Since the standard form of a complex number is ... more
Verified Answer ✓
; Since the standard form of a complex number is ... more
Verified Answer ✓
; Use DeMoivre’s Theorem to evaluate . ; ... more
Verified Answer ✓
; Use DeMoivre's Theorem to evaluate . ; ... more
Verified Answer ✓
Write the trigonometric form of the given complex ... more
Verified Answer ✓
Write the trigonometric form of the given complex ... more
Verified Answer ✓
, ; Calculate the modulus of the complex number ... more
Verified Answer ✓
, ; Calculate the modulus of the complex number ... more
Verified Answer ✓
, ; Calculate the modulus of the complex number ... more
Verified Answer ✓
, ; Calculate the modulus of the complex number ... more
Verified Answer ✓
, . ; Calculate the modulus of the complex number... more
Verified Answer ✓
, ; Calculate the modulus of the complex number ... more
Verified Answer ✓
, ; Calculate the modulus of the complex number ... more
Verified Answer ✓
, ; Calculate the modulus of the complex number ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
; Simplify the given equation.Write the complex ... more
Verified Answer ✓
; ; ; Write the solutions of the given equation... more
Verified Answer ✓
; ; ; ; ; Write the solutions of the given ... more
Verified Answer ✓
Verified Answer ✓
; ; ; ; Write the solutions of the given equation... more
Verified Answer ✓
; ; ; ; ; ; Write the solutions of the given ... more
Verified Answer ✓
; ; ; Write the solutions of the given equation... more
Verified Answer ✓
Verified Answer ✓
; Substitute the given value of and in the ... more
Verified Answer ✓
Verified Answer ✓
; Substitute for and for in the given formula... more
Verified Answer ✓
; Substitute the given values of and in the ... more
Verified Answer ✓
; Substitute the given value of and in the ... more
Verified Answer ✓
; Substitute the given value of and in the ... more
Verified Answer ✓
False, as the 9th root of is . ; The complex ... more
Verified Answer ✓
False, as the solution does not satisfy the given ... more
Verified Answer ✓
True; as one of the modulus or both have to be 0 ... more
Verified Answer ✓
False; as the th roots of complex numbers lies on ... more
Verified Answer ✓
; Divide the given complex numbers.Multiply by ... more
Verified Answer ✓
Entire Proof Answer: ; is the complex conjugate ... more
Verified Answer ✓
Verified Answer ✓
; Multiply by . ; Replace by and by . ; more
Verified Answer ✓
Substitute 0 for and for into the given Euler’s... more
Verified Answer ✓
Verified Answer ✓
16; : 2 ; The maximum displacement from ... more
Verified Answer ✓
; : ; The maximum displacement from equilibrium is... more
Verified Answer ✓
; : ; The maximum displacement from equilibrium is... more
Verified Answer ✓
; : ; The maximum displacement from equilibrium is... more
Verified Answer ✓
: ; : ; : ; The sum of interior angles of the ... more
Verified Answer ✓
: : ; : ; The sum of interior angles of the ... more
Verified Answer ✓
; ; ; The sum of interior angles of the triangle ... more
Verified Answer ✓
; To calculate the angle , substitute for and ... more
Verified Answer ✓
; ; ; Convert the given angles and into degrees... more
Verified Answer ✓
: ; : ; : ; Convert the given angles and to ... more
Verified Answer ✓
: ; : ; : ; Sum of the interior angles of a ... more
Verified Answer ✓
Case 1:Case 2: ; To find the height substitute 10... more
Verified Answer ✓
Case 1:: ; : ; : Case 2:: ; : ; : ; To find the ... more
Verified Answer ✓
No such triangle exists. ; Draw a sketch of the ... more
Verified Answer ✓
square units ; Use the area of a triangle, .... more
Verified Answer ✓
square units ; Use the area of a triangle, .... more
Verified Answer ✓
square units ; Use the area of a triangle, ..... more
Verified Answer ✓
square units ; Use the area of a triangle, ... more
Verified Answer ✓
31 feet ; Let the height of the tree be . ; Sum ... more
Verified Answer ✓
feet ; Assume the width of the river to be .Draw ... more
Verified Answer ✓
:; : ; : ; Apply the alternative form of law of ... more
Verified Answer ✓
: ; : ; : ; Apply the alternative form of law of ... more
Verified Answer ✓
: ; : ; : ; Apply the standard form of laws of ... more
Verified Answer ✓
: ; : ; : ; Apply the alternative form of law of ... more
Verified Answer ✓
; Use the law of cosine to find the third side, ... more
Verified Answer ✓
; Use the law of cosine to find the third side... more
Verified Answer ✓
ftft ; Draw the diagram of a parallelogram. It is ... more
Verified Answer ✓
m ; The two angles at B form a supplementary pair ... more
Verified Answer ✓
square units ; Substitute , and in the formula ... more
Verified Answer ✓
square units ; Substitute , and in the formula ... more
Verified Answer ✓
square units ; Substitute , and in the formula ... more
Verified Answer ✓
square units ; Substitute , and in the formula ... more
Verified Answer ✓
Calculate the magnitude of the two vectors.Also, ... more
Verified Answer ✓
Calculate the magnitude of the two vectors.Also, ... more
Verified Answer ✓
; The terminal point is and the initial point ... more
Verified Answer ✓
; The initial point is and terminal point is . ... more
Verified Answer ✓
; The initial point is and terminal point is... more
Verified Answer ✓
; The initial point is and terminal point is... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
; To get the component form of the vector ... more
Verified Answer ✓
; To get the component form of the vector ... more
Verified Answer ✓
; To get the component form of the vector ... more
Verified Answer ✓
; Multiply the vector by to get . ; Multiply ... more
Verified Answer ✓
Magnitude of unit vector is 1. ; Substitute in ... more
Verified Answer ✓
Magnitude of the unit vector is 1. ; Substitute ... more
Verified Answer ✓
Magnitude of the unit vector is 1. ; Substitute ... more
Verified Answer ✓
Magnitude of the unit vector is 1. ; Write the ... more
Verified Answer ✓
; Write the component form of the vector having ... more
Verified Answer ✓
; Write the component form of the vector having ... more
Verified Answer ✓
: 7; ; Compare the given value of to to ... more
Verified Answer ✓
: 3; ; Compare the given value of to to ... more
Verified Answer ✓
: : ; To find the magnitude of the given ... more
Verified Answer ✓
: : ; To find the magnitude of vector , ... more
Verified Answer ✓
; ; Write the given vector in component form. ; ... more
Verified Answer ✓
: : ; To find the magnitude of vector , ... more
Verified Answer ✓
: lb: ; Sketch the graphical representation of ... more
Verified Answer ✓
tension in each rope ; Let the tension acting on ... more
Verified Answer ✓
tension in each cable ; Assume that tension acting... more
Verified Answer ✓
The resultant speed of airplane: ; direction angle... more
Verified Answer ✓
; Substitute for , for , for , 7 for , for , ... more
Verified Answer ✓
; Substitute for , for , for , 12 for , for , ... more
Verified Answer ✓
7 ; Write the given vector in the component form... more
Verified Answer ✓
52 ; Write the given vector in the component form... more
Verified Answer ✓
52;Scalar ; To find , perform the dot product of ... more
Verified Answer ✓
;Scalar ; To find , perform the dot product of ... more
Verified Answer ✓
;Vector ; To find , substitute 6 for , for , 2 ... more
Verified Answer ✓
;Vector ; To find , substitute 6 for , for , 2 ... more
Verified Answer ✓
; To calculate the magnitude of vector , ... more
Verified Answer ✓
; To calculate the magnitude of vector , ... more
Verified Answer ✓
; Write the vector in component form. ; ... more
Verified Answer ✓
; Write the vector in component form. ; ... more
Verified Answer ✓
Apply the formula of an angle between two vectors... more
Verified Answer ✓
Apply the formula of an angle between 2 vectors ... more
Verified Answer ✓
; Apply the formula of an angle between 2 vectors... more
Verified Answer ✓
: ; Apply the formula of an angle between 2 ... more
Verified Answer ✓
Calculate the dot product of and . The vectors ... more
Verified Answer ✓
Orthogonal ; Find the dot product of vectors and... more
Verified Answer ✓
Neither orthogonal nor parallel ; Find the dot ... more
Verified Answer ✓
Parallel ; Find the dot product of vectors and .... more
Verified Answer ✓
; Write vectors and into component form. ; ... more
Verified Answer ✓
; Write vectors and into component form. ; ... more
Verified Answer ✓
Verified Answer ✓
8 ; Write the component form of the given vectors... more
Verified Answer ✓
; Apply the formula for projection of on . ; ... more
Verified Answer ✓
; Find the projection of on . ; Let be the ... more
Verified Answer ✓
; Find the projection of on . ; Let be the ... more
Verified Answer ✓
; Find the projection of on . ; Let be the ... more
Verified Answer ✓
72,000 ft-pounds ; Let be the displacement vector... more
Verified Answer ✓
104 lbs ; The gravitational force acts in the ... more
Verified Answer ✓
; On comparing the complex number to , the ... more
Verified Answer ✓
; On comparing the complex number to , the ... more
Verified Answer ✓
7 ; On comparing the complex number to , the ... more
Verified Answer ✓
6 ; On comparing the complex number to , the ... more
Verified Answer ✓
; Calculate the absolute value, , of the given ... more
Verified Answer ✓
; Calculate the absolute value, , of the given ... more
Verified Answer ✓
; Substitute for and for into to determine ... more
Verified Answer ✓
; Substitute for and 3 for into to determine ... more
Verified Answer ✓
; Use the product rule to determine the product ... more
Verified Answer ✓
; Use the product rule to determine the product ... more
Verified Answer ✓
; Use the quotient rule for complex numbers. ; ... more
Verified Answer ✓
; Use the quotient rule for complex numbers. ; ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
; Use Demoivre's Theorem to obtain the indicated ... more
Verified Answer ✓
; Use Demoivre's Theorem to obtain the indicated ... more
Verified Answer ✓
; Substitute 2 for and 3 for into to determine... more
Verified Answer ✓
; Substitute 1 for and for into to determine... more
Verified Answer ✓
; Substitute for and 1 for into to determine ... more
Verified Answer ✓
; Substitute for and for into to determine ... more
Verified Answer ✓
; Substitute 0 for and for into to determine ... more
Verified Answer ✓
; Substitute 0 for and for into to determine ... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
; Subtract 256 from both sides of the given ... more
Verified Answer ✓
; Add to both sides of the given equation and ... more
Verified Answer ✓
; Subtract from both sides of the given equation... more
Verified Answer ✓
; Subtract 81 from the given equation and rewrite... more
Verified Answer ✓
True, because the value of is definite. This ... more
Verified Answer ✓
False, because it may be possible that the ... more
Verified Answer ✓
; Since the sum of the three angles of a triangle... more
Verified Answer ✓
; Since the given information resembles case, ... more
Verified Answer ✓
; Since the given information resembles case, ... more
Verified Answer ✓
; Since the sum of the three angles of a triangle... more
Verified Answer ✓
; Since the given information resembles case, ... more
Verified Answer ✓
No triangle exists. ; Apply the law of sines. Use... more
Verified Answer ✓
; Since the length of two adjacent sides and the ... more
Verified Answer ✓
; Substitute 55 for , 85 for and 100 for in ... more
Verified Answer ✓
; Let be and be Substitute for , for , 4 for... more
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
Verified Answer ✓
; Write the formula for unit vector in the ... more
Verified Answer ✓
; First, find a unit vector in the direction of... more
Verified Answer ✓
pound ; Write the first force in the form of ... more
Verified Answer ✓
; Write the definition of dot product of two ... more
Verified Answer ✓
; Write the given vectors, and , in the ... more
Verified Answer ✓
Yes, the dot product of vectors and is 0. This ... more
Verified Answer ✓
; Calculate the projection vector by ... more
Verified Answer ✓
; Calculate the absolute value of by ... more
Verified Answer ✓
; Apply the trigonometric cofunction identity to ... more
Verified Answer ✓
; Apply DeMoivre’s theorem in the given ... more
Verified Answer ✓
; Calculate the absolute of the given expression ... more
Verified Answer ✓
: ;: ;: ;: ; ; Calculate the absolute value of the... more
Verified Answer ✓
= = = = ; Add to both sides of the given ... more
Verified Answer ✓
Verified Answer ✓
; Multiply by to convert radians into degrees... more
Verified Answer ✓
; Substitute the given value of to calculate ... more
Verified Answer ✓
The period of is .Compare the given equation, , ... more
Verified Answer ✓
The period of is .Compare the given equation, , ... more
Verified Answer ✓
Start by sketching the graph of . Compare the ... more
Verified Answer ✓
; From the given graph, it can be observed that ... more
Verified Answer ✓
Undefined ; Consider to be . Thus, is equal to 3... more
Verified Answer ✓
; Consider to be . Thus, is equal to . ; Since ... more
Verified Answer ✓
; Consider to be . Thus, is equal to . ; Since... more
Verified Answer ✓
; Determine the LCM and simplify the given ... more
Verified Answer ✓
Use Pythagoras identity for the left side of the ... more
Verified Answer ✓
Use the sum and difference formula to rewrite the ... more
Verified Answer ✓
Multiply the numerator and denominator of the left... more
Verified Answer ✓
; Rewrite the equation and factorize in terms of ... more
Verified Answer ✓
; Rewrite the equation and use reciprocal ... more
Verified Answer ✓
; ; Rewrite the equation by substituting for .... more
Verified Answer ✓
; ; Enter the equation in the graphing utility. ... more
Verified Answer ✓
Approximate zeros: and Exact zeros: and ; Enter ... more
Verified Answer ✓
; Use the quotient identity to find out the ... more
Verified Answer ✓
; The tangent of angle is positive if lies in ... more
Verified Answer ✓
; Use pythagoreans identity to find cosine of ... more
Verified Answer ✓
; Use the sum to product formula,, to write the ... more
Verified Answer ✓
Entire Proof Answer: Simplify the left side of the... more
Verified Answer ✓
Entire Proof Answer: Simplify the left side of the... more
Verified Answer ✓
Entire Proof Answer: Simplify the left side of the... more
Verified Answer ✓
Entire Proof Answer: Use the sum and difference ... more
Verified Answer ✓
; For the given triangle , the law of sines is ... more
Verified Answer ✓
; For the given triangle , the law of cosines is ... more
Verified Answer ✓
B = ; The sum of all angles of a triangle is . To ... more
Verified Answer ✓
; ; ; Substitute 24 for a , 30 for b, and 47 for c... more
Verified Answer ✓
; The formula to calculate the area of a triangle... more
Verified Answer ✓
; Substitute 30 for , 41 for , and 45 for into... more
Verified Answer ✓
; Any vectors can be written as a linear ... more
Verified Answer ✓
; The unit vector of is equal to vector divided... more
Verified Answer ✓
; The dot product of two vectors and is equal ... more
Verified Answer ✓
1 ; For orthogonal vectors and , the dot product ... more
Verified Answer ✓
; For any non-zero vectors and , the projection ... more
Verified Answer ✓
; The complex number can be written in a ... more
Verified Answer ✓
; Substitute for and for in the given complex ... more
Verified Answer ✓
; Apply the formula to multiply two complex ... more
Verified Answer ✓
; To rewrite the complex number in trigonometric ... more
Verified Answer ✓
1, , ; Write 1 as a trigonometric form of complex ... more
Verified Answer ✓
; Rewrite the given equation in trigonometric ... more
Verified Answer ✓
5 feet ; Draw a diagram from the given data.... more
Verified Answer ✓
; A simple harmonic motion in the form of or ... more
Verified Answer ✓
; Draw the angle representing the airplane ... more
Verified Answer ✓
; Express the force as a diagram. ; Angles A and ... more