Sequences & Series Questions and Answers

Evaluate each expression. 9) log₆₄ 4 10) log₂₇ 1/3 11) log₉ 1/81

A school choir needs to make T-shirts for its 75 members and has set aside some money in their budget to pay for them. The members of the choir decided to order from a printing company that charges $3 per shirt, plus a $50 fee for each color to be printed on the shirts. 1. Write an equation that represents the relationship between the number of T-shirts ordered, the number of colors on the shirts, and the total cost of the order. If you use a variable, specify what it represents.

Simplify. (Assume all variables are nonnegative.) (3√2x - √3x) - (√2x - 7√3x) Provide your answer below:

Select the factors that multiply to create a polynomial. with this description: (1) Leading term is 5x⁴ (2) Has four real roots (3) Has zeros at x = 1 and x = -2 (Select all that apply) (a) 5 (b) x (c) (x - 1) (d) (x - 2) (e) (x + 2) (f) (x + 7)

Consider the difference equation yt+1(a+byt) = cyt, t = 0,1, .... , where a, b, and c are positive constants, and yo > 0. Show that yt > 0 for all t. Define xt = 1/yt. Show that by using this substitution the equation turns into the canonical form. Solve the difference equation yt+1(2+3y) = 4yt, assuming that yo =1/2. What is the limit of y, as t → ∞?

Given that g(x)=x²-2x-6, find (g o g)(-3).

A parabola can be drawn given a focus of (-8,-5) and a directrix of x = -2. What can be said about the parabola?

Let A be a 7 x 6 matrix such that Ax = 0 has only the trivial solution. Find the rank and nullity of A. Let A be a 5 x 7 matrix with rank 4. a. What is the dimension of the solution space of Ax = 0? b. Is Ax = b consistent for all vectors b in R⁵? Explain.

Write a cosine function that has a midline of 2, an amplitude of 5 and a period of 4/3.

Zombies lose limbs. Mutants grow limbs. Mutant-zombies do both. Today, a certain mutant-zombie grew 5 limbs, lost 12 limbs, and grew another 2 limbs. What is the change in number of limbs the mutant-zombie has compared to yesterday?

Solve tan(x)=-√5 on 0≤x<2π There are two solutions, A and B, with A<B A = B = Give your answers accurate to 4 decimal places

Jerome will be buying a used car for $10,000 in 2 years. How much money should be ask his parents for now so that if he invests it at 10% compounded continuously, he will have enough to buy the car?

State the amplitude, period, and increment for each function. Then graph. y=-3 sin 2x Amplitude: Period: Increment: y = 2 cos 2x Amplitude: Period: Increment:

A new car is purchased for $18, 000 and over time its value depreciates by every 4 years. What is the value of the car 17 years after it was purchased, to the nearest hundred dollars? one half

Determine the order of each of the following quotient groups. 1. (a) Z₈ /([4]) 2. (a) Z₈/([3])

Express the equation in exponential form (a) log₂ 4 = 2. That is, write your answer in the form 2 ᵃ =B then A =___ and B =____ (b) log₅125 = 3. That is, write your answer in the form 5ᶜ=D C =__ and D =___

Determine all possible exact values of θ between 0 degrees and 360 degrees that satisfy the equation sinθ =cos150°.

Prove that limx→0 sin(1/x) does not exist in R.

Simplify 1 + cot(t)/(1 + tan(t)) to a single trig function. a) Use Reciprocal Identities to rewrite the expression to only have sine, cosine or tangent funciton. b) Times an appropriate trig function to get rid of the complex fraction. c) Cancel the common fator between the numerator and denominator. d) Express the final answer without fraction. 1 + cot(t)/(1 + tan(t))=___

Anna invested $28,000 in an account paying an interest rate of 6.5% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $39,500?

Write the sum without sigma notation and find its sum. k=0Σ10 1/(k + 1)(k + 2)

Given that sin(a) = 1/3 and cos(b)= -2/6 with a and b both in the interval [π/2, π] find the exact values of sin(a + b) and cos(a − b). Step 1: Since sin(a)= 1/3 and a in the interval [π/2, π] cos(a) Step 2: Since cos(b) = -2/6 and b in the interval [and b in the interval/2, and b in the interval] Step 3: cos(a - b) =

A plane has an airspeed of 127 km/h. It is flying on a bearing of 71° while there is a 20 km/h wind out of the northeast (bearing 225°) What are the ground speed and the bearing of the plane? The ground speed is km/h. (Round to the nearest tenth as needed)

Evaluate the following expression. DNE if the expression is undefined. a) arcsin ( sin(( 38π/8 )) =_____ b) arccos(cos(3π/8 ))=___ c) cos‾¹( sin(5π/3)=___

Decide whether it would be more convenient to solve the system of equations by substitution or elimination. 3x+8y=-13 14x +3y/5 = -10 Select the correct answer below: O elimination O substitution

sin(θ) =-9/41 where 3π/2< θ < 2π. Use the given information about to find the exact value of cos(2θ).

Express the equation in logarithmic form: (a) 4² = 16 is equivalent to log₄ A = B. A = and B= (b) 10^(-4) = 0.0001 is equivalent to log₁₀ C = D. C = and D =

Simplify (-8√3+6√15) - (√3-√15). Provide your answer below:

Determine the parametric equation of a line that goes through A(3,5,7) and is perpendicular to the line (3,-5,2) +t(3,-3,3)

Calculate the perimeter of the triangle formed by the following set of vertices. {(-2,-2), (2, 2), (3,-7)}

Let f(x) = 2x - 1 and g(x) = x² – 4. Find (f o g)(-2). Then (f o g)(-2) = ______

In (r, q) coordinates A = (83.0, 344 degrees) and B = (69.0, 2.90E2 degrees). Given R = A - B (a) In polar coordinates the resultant vector is R =)Rr, Rθ) What is the radial component, Rr? (b) In polar coordinates the resultant vector is Rr, Rθ. What is the angular component, Re in degrees? Number

Simplify √a³b³

Simplify the expressions below as much as possible. Leave no negative numbers under radicals. √(-27)/√(-9) = √(-20).√(-5) =

Simplify: √(48a⁵b³). Present the answer in the simplest way. Provide your answer below:

Find how much money needs to be deposited now into an account to obtain $3,700 in 5 years, if the interest rate is 3.5% per year compounded continuously.

What is tan 11π\6 ? A.)-√3/3 B )√3/3 C.)-√3 D.)√3

Determine the amplitude and period of the function y = 3 sin(2x). Then, graph the function over its single period using five key points.

Use the equation ý = 16.665 -0.21x to find the value of ŷ given x = 48. Round the result to the nearest tenth. ŷ=____

Find the equation of the tangent line to the curve y = 3 sec x - 6 cos x at the point (π/3, 3). The equation of this tangent line can be written in the form y = mx + b where m is: ____ and where b is: ____ Let h(t) = tan(2x + 3). Then h'(5) is ____ and h''(5) is ____

The observed bunny rabbit population on an island is given by the function p=-0.4t² + 130t + 1200 where t is the time in months since they began observing the rabbits. 1. When is the maximum population attained? 2. What is the maximum population? 3. When does the bunny rabbit population disappear from the island?

Evaluate: - ⁵√(243). Provide your answer below:

Write the expression log₂(x³ ∜y¹¹) as a sum of logarithms with no exponents or radical.

Calculate the distance between (-1/2,2) and (5/3,-2/3).

Number of Brokers Who Sold x Houses in June. x 1 2 3 4 5 6 Number of Brokers 8 4 3 4 1 1 The table above shows the number of rokers in a real estate agency who sold x houses in June, for x from 1 to 6. What was the median number of houses sold per broker that month for the 21 brokers? 2 2.5 3 3.5 4

Find the point that is symmetric to the point (4, -2) with respect to the x-axis, the y-axis, and the origin. The point symmetric to (4, -2) with respect to the x-axis is (Type an ordered pair.)

Solve the system by graphing: y<3x +2 y>-x-1 Solve the system by graphing: x>-4x -2 y≥-4

Steve wants to grow his $45000 savings to $59000 before his travels around the world. How long will this take if the bank is offering 6.1% annual interest compounded monthly? Round your answer to the nearest tenth.

Drag each tile to the correct box. Arrange the complex numbers in order according to the quadrant in which they appear, starting with the first quadrant. 3-4i -1-3i 4+i -2 + 2i _____->______→_______->______

Graph polynomial function f(x)=x³+5x²-x-5 by finding zeros, y intercept, end behavior, and other pertinent information. All work must be shown algebraically.