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⟩