Flick Final Review

Find two sets of polar coordinates with 0≤θ<2π for the point (-2,0), given in rectangular coordinates.

(-2,0), (2,π)

Solve the system of linear equations. 2x-2y+3z=-21 2x+z=-11 -2x+4y-4z=28

(-4, 2, -3)

Determine the domain of g(x)=1/x²-49

(-♾️,-7)u(-7,7)u(7,♾️)

Convert the point from polar polar coordinates to rectangular coordinates. Round answer to three decimal places, if necessary. (3, -3π/2)

(0, 3)

Solve the system by the method of elimination. Round numbers to three decimal places {5.2x+8.1y=6.9 -2.6x+1.1y=-0.7

(0.495, 0.534)

Solve the system by the method of elimination 5x-y=11 -7x-y=-25

(3, 4)

Solve the system of linear equations. x+y+z=-6 x-6y-7z=76 8y-6z=-18

(5, -6, -5)

Find f ° g f(x)=x+2, g(x)=5/x²-4

(f ° g)(x)=2x²-3/x²-4

Find f ° g f(x)=3x-2, g(x)=x-5

(f ° g)(x)=3x-17

Find the standard form of the equation of the ellipse with the given characteristics vertices: (4, -6), (4, 10) minor axis of length: 4

(x-4)²/4 + (y-2)²/64 =1

Find the standard form of the parabola with the given characteristics. focus: (8, 13) directrix: y=-1

(x-8)²=28(y-6)

Find the point (x,y) on the unit circle corresponding to the real number 11π/6

(√3/2, -1/2)

Simplify (-4+i)(4-5i) and write the answer in standard form

-11+24i

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is to the correct angle mode.) Sec(-5π/8)

-2.6131

Find all real values of x such that f(x)=0 f(x)=-3x-2/5

-2/3

Determine whether the sequence is geometric. If so, find the common ratio. -2,6,-18,54,...

-3

Find the indicated nth term of the geometric sequence. 5th term: a³=-3/16, a⁹=-3/65,536

-3/256

Find the domain f(y)=√9-y²

-3≤y≤3

Given vectors u=⟨-2, -3⟩ and v=⟨4, -4⟩, determine the quantity indicated below. -4u⋅3v

-48

Find the sum of the integers from -34 to -12.

-529

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) tan1.7

-7.6966

Simplify (3-6i)²-(3+6i)² and write the answer in standard form

-72i

Use a double angle formula to rewrite the following expression. -16sin(x)cos(x)

-8sin(2x)

Given u=-3i-2j and v=-i-5j, determine -9u+6v

-9u+6v=27i-21j

SImplify the given expression algebraically. cos |π+x|

-cos x

Solve the equation below algebraically. Round your result to three decimal places. 3+ln x/x²=0

.050

Find the zeroes of the function below algebraically, if any exist f(x)=25x³-60x²+36x

0 and 6/5

You are given the probability that an event will happen. Find the probability that the event will not happen. P(E)=0.33

0.67

Solve the logarithmic equation below algebraically. log base 6 (2x+4)=log base 6 (5x+1)

1

Write the first five terms of the sequence. (Assume that n begins with 0.) aⁿ=3ⁿ/(n+1)!

1, 3/2, 3/2, 9/8, 27/40

Solve the exponential equation below algebraically. Round your result to three decimal places. e²ˣ+3eˣ-18=0

1.099

Approximate tan⁻¹(3). Round your answer to four decimal places.

1.2490

Identify the x-intercept of the function y=3+log base 4 x

1/64

FInd the probability for the experiment of drawing two marbles (without replacement) from a bag containing four green, six yellow, and five red marbles such that both marbles are yellow.

1/7

Rewrite the angle 2π/3 radians in degree measure.

120°

Find the exact value of sec(arctan 8/15)

17/15

Determine two coterminal angles (one positive and one negative) for θ=5π/6

17π/6, -7π/6

Find the exact value of ln e².⁵⁰ -ln√e without using a calculator

2

Solve the equation f(x)=g(x) algebraically. f(x)=ln e³ˣ⁻⁹ g(x)=x-5

2

Given a=5, b=9, and c=12, use Heron's Area Formula to find the area of triangle ABC. Round Answer to two decimal places.

20.40 sq. units

Simplify 4+3i/5+2i and write the answer in standard form

26/29+7/29i

A triangular parcel of land has sides of lengths 100, 580, and 600 feet. Approximate the area of the land. Round answer to the nearest foot.

28,800 ft²

Expand the expression below and use fundamental trigonometric identities to simplify. (sin(ω)+cos(ω))²

2sin(ω)+cos(ω)+1

Rewrite the given angle in radian measure as a multiple of π. (Do not use a calculator.) 72°

2π/5

FInd the sum of the integers from -1 to 27

377

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that n begins with 1.) aⁿ=-6+4n

4

In the following triangle, A=58°, b=105, and a=126. Use the Law of Sines to find the measure of angle C, in degrees. Round your answer to two decimals.

40.42°

Determine a pair of angles (one positive and one negative) in degree measure coterminal to the angle 117°

477°, -243°

Find the reference angle θ for the given angle θ. θ=312°

48°

Rewrite the logarithmic equation log base 4 1/16=-2 in exponential form

4⁻²=1/16

Find the value(s) of x for which f(x)=g(x) f(x)=x²-7x+3, g(x)=-3x+8

5, -1

Write the first five terms of the arithmetic sequence. a¹=5, d=7

5, 12, 19, 26, 33

Find (if possible) the complement of π/7

5π/14

Given a=12, b=8, and c=11, use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

63.06°

Evaluate ⁸P⁵

6720

FInd the specified nth term in the expansion of the binomial. (Write the expansion in descending powers of x.) (2x-3y)⁸, n=5

6720x^3y^5

Use the trigonometric substitution x=8sec(θ) to write the expression √x²-64 as a trigonometric function of θ, where 0<θ<π/2

8tan(θ)

Indentify the center and radius of the circle below. (x+1)²+(y-8)²=9

Center: (-1, 8) Radius: 3

A submarine, cruising at a depth d=65 meters, is on a trajectory that passes directly below a ship (see figure). If θ is the angle of depression from the ship to the submarine, find the distance L from the ship to the sub when θ=70°. Round to the nearest meter.

L=84 meters

Determine the domain of f(x)=6x+6/x²-6x

all real numbers except x=0 and x=6

Find a formula for aⁿ for the arithmetic sequence a³=19, a¹³=99

aⁿ=-5+8n

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) -5,-2, 1, 4, 7

aⁿ=3n-8

GIven A=52°, B=65°, and a=7.1, use the Law of SInes to solve the triangle for the value of b. Round answer to two decimal places.

b=8.17

GIven A=54°, B=69°, and a=7.1, use the Law of SInes to solve the triangle for the value of b. Round answer to two decimal places.

b=8.19

FInd the center and foci of the ellipse. (x-9)²/32 + (y+5)²/36=1

center: (9, -5) foci: (9, -7) (9, -3)

Use a double-angle formula to find the exact value of cos 2u when sin u=8/17, where π/2<u<π

cos(2u)=161/289

Find the exact value of cos(u+v) given that sin u=5/13 and cos v=-4/5. (Both u and v are in Quadrant II)

cos(u+v)=33/65

If sin x=1/2 and x=√3/2, evaluate the following function. cscx

csc x=2

Classify the graph of the equation below as a circle, a parabola, an ellipse, 2x²+5y²+8x-2y=0

ellipse

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. -3, -1, 0, 1, 3

f(x)=x⁵-10x³+9x

Determine the equations of any horizontal and vertical asymptotes of f(x)=x²/x²+16

horizontal: y=1; vertical: none

Rewrite the logarithm log base 4 25 in terms of the natural logarithm.

ln 25/ ln 4

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variable are positive.) ln(x/∛x⁵-2)

ln x-1/3 ln(x⁵-2)

Determine whether the sequence is geometric. If so, find the common ratio. -1,2,5,8,...

not geometric

Write the given expression as the sine of an angle. sin85°cos50°+sin50°cos85°

sin(135°)

Find the vector v that has a magnitude of 4 and is in the same direction as u, where u=(-5, -3)

v=(-20/√34, -12/√34)

FInd the vector v that has a magnitude of 6 and is in the same direction as u, where u=⟨-6, -5⟩

v=⟨-36/√61, -30/√61​⟩

Find the component form of vector v with initial point (-5, 1) and terminal point (-3, -2)

v=⟨2,−3⟩

Find the vertex and focus of the parabola x²-8y=0

vertex: (0, 0) focus: (0, 2)

Use the Binomial Theorem to expand and simplify the expression (w-2)⁵

w⁵-10w⁴+40w³-80w²+80w-32

Write an algebraic expression that is equivalent to sin(arctan x/9)

x/√x²+81

Find all the zeroes of the function f(x)=(x+6)(x+3i)(x-3i)

x=-6, -3i, 3i

Determine the zeros (if any) of the rational function f(x)=x²-64/x+5

x=-8, x=8

Determine which x-value below is a solution of the equation log base 7 (5/3 x)=3

x=1029/5

Which equation does not represent y as a function of x?

x=6

Which set of parametric equations represents the graph of the following rectangular equation using t=6-x? y=x²+2

x=6-t y=(6-t)²+2

Solve the following equation tan x-√3=0

x=π/3+nπ, where n is an integer

Find all solutions of the following equation in the interval [0, 2π). csc²x=cot x+1

x=π/4, π/2, 5π/4, 3π/2

Find the exact solutions of the given equation in the interval [0, 2π) 2sin²x+sinx=1

x=π/6, 5π/6, 3π/2

Use long division to divide. (x³+3x²+x+3)÷(x+3)

x²+1

Slope intercept form of this line Point: (-4,7) Line: -5x-15y=-6

y=3x+19

Find the slope-intercept form of the line passing through the points (-1,-6),(0,-2)

y=4x-2

Given the equation below, determine two solutions such that 0°≤θ≤360° sinθ=-√3/2

θ=240°,300°

Solve the following equation. 3csc²(x)-4=0

π/3+πn, 2π/3+πn, where n is an integer

Solve the multi-angle equation below. sin(2x)=√3/2

π/6+nπ, π/3+nπ, where n is an integer

Find the amplitude of y=-π/7cos(3x/2)

π/7

Find the inverse function of f. f(x)=x⁵+5

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎_____ f⁻¹(x)=⁵√x-5

Write an algebraic expression that is equivalent to tan(arccos3x).

√1-9x²/3x

Evaluate the tangent of the angle without using a calculator. -120°

√3

Let u=⟨6,5⟩ and v=⟨12,7⟩. Find u-v.

⟨-6, -2⟩