pre calc final

Find the resultant vector of A - B where A = (-2, -3) and B = (2, 7).

(-4, -10)

What is the midpoint of line segment AD?

(1.5,1)

Rewrite 6 + 8i in polar form.

10(cos53.13°, isin53.13°)

(5 - 3i) + (6 + 5i) =

11 + 2i

For the ordered pairs (x, y) that satisfy both equations, what is the sum of the x and y values?

14

Convert 453° to radians.

151pi/60 or B

The angle of depression from the top of a lighthouse to a boat in the water is 30°. If the lighthouse is 89 feet tall how far is the boat from the lighthouse to the nearest foot?

154 feet

How many solutions does the system have?

2

The imaginary number i is equal to sqr −1 which expression is equivalent to (6 + 5i) − (4 + 4i)?

2 + i

If vector v = <5, -9>, what is its direction?

299.1°

A building is 190 feet tall and has a shadow that is also 190 feet. Determine the angle of elevation from the tip of the shadow to the top of the building.

45°

Which system of equations could the matrix equation _ represent?

4x - 7y = 19 and 9x + y = 26

The imaginary number i is equal to sqr −1 which expression is equivalent to −(3 + 4i) + (8 + 7i)?

5 + 3i

Which of these is equivalent to 450°?

5pi/2 rad or C

convert 7pi/21 to degrees

60°

Multiply (4 - 3i)2.

7 - 24i

Given ΔABC, m∠A = 50°, m∠B = 60°, and a = 7. Find b.

7.9

Find the angle that the vector v = <2, 6> makes with the positive x-axis.

71.6°

Find the direction of the sum of v and u if v = <2,3> and u = <-1,4>. Round to the nearest hundredth of a degree.

81.87°

A tree casts a shadow that is 150 feet long. If the angle of elevation from the tip of the shadow to the top of the tree is 30°, how tall is the tree to the nearest foot?

87 feet

Given vector a = <2, 3> and vector b = <−7,5>Find the magnitude of the resultant vector a + b.

9.433

Suppose that ||v|| = 4 and the direction of v is 140°. What are the vector's x and y lengths correct to the nearest hundredth?

<-3.06, 2.57>

If v = <−4, 7>, what is −3v?

<12, −21>

If v = <9, -6> and w = <-4, -2>, find v - w.

<13, -4>

Find the components of a vector with an initial point of (5, −2) and a terminal point of (3, −2).

<−2, 0>

Find the components of a vector with an initial point of (8, −3) and a terminal point of (4, −6).

<−4, −3>

Which graph represents vector <3, 2>?

A

Write the standard equation for the ellipse with the following conditions: foci: (0, 2) and (0, 8)vertices: (0, 0) and (0, 10)

A

Write the equation of the parabola with vertex (3, 4) and focus (5, 4).

A) (y - 4)^2 = 8(x - 3)

Suppose θ is an angle in standard position whose terminal side lies in Quadrant II.If cos θ = −2/3, find the value of tan θ.

A) -sqr5/2

Find the first two positive solutions to tan x = 1

A) pi/4 and 5pi/4

Give polar coordinates for the point with Cartesian coordinates (3, 3).

(3 sqr2, pi over4

Find all point(s) of intersection of the line y = 4x and the parabola y = x2 - 2x + 9.

(3, 12)

The midpoint of segment AB is (1, 4). The coordinates of point A are (-2, -3). Find the coordinates of point B.

(4, 11)

Give the Cartesian coordinates for the point with polar coordinates (r, Θ).

(r2cosΘ, r2sinΘ)

Which matrix has an inverse?

(the same) B

Which ordered pair (x, y) satisfies both equations y = x2 + 6 and x = 6 − y?

(−1, 7)

Find the exact value, it it exists. tan(3π4)

-1

What is the midpoint between (-2 - 5i) and (1 + 3i)?

-1/2 - i

Which is equivalent to (-1 + 2i)(5i)?

-10 - 5i

Simplify completely:

-9+3i/5 or D

If sin(x) = B, then sin(x + π) =

-B

Suppose θ is an angle in standard position whose terminal side lies in Quadrant III.If cos θ = −2/5 find the value of sin θ.

-sqr21/5

Solve the equation over the interval [0, 2π), stating answer(s) in radians:2cos2 x - cosx - 1 = 0

0, 2pi/3, 4pi/3

The imaginary number i is equal to sqr −1 which expression is equivalent to (3 + 7i) − (2 + 9i)?

1 − 2i

Simplify.

1-2i

The graph of a function is shown. Which function is graphed?

A) y = sin (x) + 1

Find the exact value, it it exists. sin(5π/3)

B

A ball is thrown with an initial velocity of 60 feet per second, at an angle of 28° with the horizontal. Find the vertical and horizontal components of the velocity.

The horizontal component is 52.98 feet per second and the vertical component is 28.17 feet per second.

Given that sinΘ = sqr3/2 and that Θ lies in quadrant I, determine the value of cosΘ.

c) 1/2

Simplify the expression.

i

Find the magnitude of the vector v = <-2, 5>.

sqr 29

What is the magnitude of the vector shown?

sqr13 or C

What is the standard form of an ellipse with foci at (0, ±2), and vertices at (0, ±4)?

x212 + y216 = 1 or B

What is the equation of the parabola that has a vertex of (3, 6) and a focus of (3, 8)?

y - 6 = 1/8(x - 3)2

What complex number is plotted on the complex plane shown?

− 2 + 3i

What is the component form of the vector shown in the graph?

⟨-4, -8⟩

What is the system of equations written in the form Ax + b, where A is a matrix and x and b are vectors?

B

Write the linear system of equations as a single matrix equation.

B

Find the exact value, it it exists. cos(7π/6)

B) -sqr3/2

If sin(Θ) = -5/8 and 180° < θ < 270°, what is the value of cos(θ)?

B) -sqr39/8

Given: ΔABC; b= 10; c = 14, and ∠A = 54°. Find the length of side a to the nearest whole number.

B) 12

A triangular plot of land has sides 205 m, 195 m, and 120 m. Find the measure of the smallest angle.

B) 34.8°

Using the triangle pictured, find the measure of angle A. Round your answer to the nearest tenth.

B) 53.0°

The circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters, what is the measure of x?

B) 60°

sin(70°) =

B) sin(50°)cos(20°) + cos(50°)sin(20°)

Find the exact value, it it exists.csc(4π/3)

B) −2sqr3/3

Find the equation of a hyperbola with vertices at (−1, 2) and (3, 2) and foci at (−5, 2) and (7, 2).

C

The circle with center O has a radius of 4 centimeters. If x = 30°, what is the length of arc AB?

C) 2π/3 cm

A ten foot long ladder leans against a wall, with the top of the ladder being eight feet above the ground. What is the approximate angle that the ladder makes with the ground?

C) 53°

sin(40°)cos(15°) - cos(40°)sin(15°) =

C) sin(25°)

tan(80°) equals which expression?

C) tan(55°) + tan(25°)/ -1 tan(55°)tan(25°)

Perform the indicated operation. 6 - 2i5 + 3i =

D

Which is the graph of y = −2sin(2x)?

D

Emma is planting a triangular rose garden. Two sides of the plot are 8 feet and 12 feet, and the angle between them is 87°. Which expression can be used to find the area of the rose garden?

D) 1/2(8)(12)sin87°

A ball is kicked with an initial velocity of 90 feet per second, at an angle of 15° with the horizontal. Find the vertical and horizontal components of the velocity.

The horizontal component is 86.93 feet per second and the vertical component is 23.29 feet per second.