Sequences & Series Questions and Answers

use a wall clock and use the minute hand of the clock as a real world periodic function. Model the height of the minute hand as a sinusoidal function. Then determine the peak and Trough of your model. Determine the period of your model. Determine the Equation of the Axis of your model. Determine the Amplitude of your model. Create a sinusoidal equation using both Sine and Cosine to model your scenario.

f(x) = 2x⁴+ 3x³ + 3x - 2 Find all the zeros of each polynomial function and write the polynomial as a product of linear factors. (a)-2, 1/2, + i; f(x) = (x - i)(x + i)(x + 2)(2x - 1) (b)2, 1/2, +- i; f(x) = (x - i)(x - i)(x + 2)(2x - 1) (c)-2, 1/2, + i; f(x) = (x + i)(x + i)(x + 2)(2x - 1) (d)-1, 1/2, + i; f(x) = (x - i)(x + i)(x + 2)(2x + 1)

Find the curvature and the radius of convergence of a x=(1/1+t),y=(1/1-t) at t=0

Solve. √x+7=4 Do not include x = in your answer. If there is no solution, the answer is the empty set Ø .

Perform the operation and simplify. Leave answers in exponential form. {5^(11/3)} / {5^(2/3)} Provide your answer below:

Simplify √6 - 4√6 + 2√6. Provide your answer below:

Which ordered pair corresponds to the y-intercept of the function F(x)=-12x/13+15? HINT: what is the y intercept, the number without the letter? A. (0, 13) B. (0, 15)

Consider the following point and line. Point Line (4,1) 9x-3y = 4 (a) Write the equation for the line through the given point and parallel to the given line. (b) Write the equation for the line through the given point and perpendicular to the given line.

Tristan bought a Pokemon card for $10. The value of the card increases by 5% each year. Write the equation for this situation. A. y= 10(1.5)ˣ B. y= 10(1.05)ˣ C. y=1.05(10)ˣ D. y=10(.95)ˣ

Which of the following expressions are equivalent to 4+ (14 - 2)? Choose 3 answers: (A) 4-(-14-2) (B) (4-14) - 2 (C) 4-(-14) - (2) (D) 4+14+ (-2) (E) -(-4-14) - 2

Sketch each of the following angles in standard position. 1) θ = -2π/3 2) θ = 11π/6 3) θ = 235°

Twenty parents at the doctors were asked the age of their first child. Age of 1 2 3 4 5 6 7 child Frequency 4 5 3 2 3 1 2 1)Create a dot plot to represent the frequency of each car age. 2)what is the mean age of the children? What is the median age?

Two different $1,000 investments are made. One is put into an account earning 8% per annum compounded annually. Another is put into an account earning 7.8% per annum compounded monthly. Compare the instantaneous rates of change 10 years after the initial deposit?

3.) a. Line segment MP is the midsegment of △LNO. NO=36. Find MP. b. LO=30, MN=9. Find the perimeter of △LMP

Element X decays radioactively with a half life of 8 minutes. If there are 170 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 5 grams?

What is the distance between (5, 75°) and (-7,127°)?

Write an equation for the nth term of each geometric sequence. 3) 64, 16, 4, ... 4) a₄ = 80, r=4

Which figures have volumes that can be found by multiplying base area times height then dividing by 3?

Find the common ratio of each sequence. 1) 10, 2, 0.4,... 2) -8,-20, 50,... 3) 0.45, 0.9, 1.8, 3.6,...

Write the definition of the apothem of a regular polygon. Write the definition of a circle.

Find the intersection of the line and plane: 3y - 4x + 3z = -42, r(t) = (0, 0, -3) + (-1, -2, -3)

Factor f(x) into linear factors given that k is a zero of f(x). f(x) = x² + 3x³ - 42x² - 172x-168; k=-2 (multiplicity 2) In completely factored form, f(x) = (Factor completely.)

Let v₁ = [1 2], V₂ = [-2 2], V₃ = [3 7], y = [5 3] a) Write y as an affine combination of the other points listed, if possible. b) Determine if the set of points S= {V₁, V₂, V₃} is affinely dependent.

Natalie invested $1,200 in an account paying an interest rate of 6.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 17 years?

Setup the iterated double integral that gives the volume of the following solid. Correctly identify the height function h = h(x, y) and the region on the xy-plane that defines the solid. The solid bounded above by z = x² + y² over the region R on the xy-plane bounded by x + 2y = 4, the x-axis and the y-axis.

$3000 is invested at an APR of 1.8% for 12 years. $10,000 is invested at an APR of 3.7% for 12 years $40,000 is invested at an APR of 2.8% for 30 years.

Two trees reside to the north. The are 24 stand the paces apart. From where you right tree is 15 paces away The left tree is 20 paces away. You feel that the angle they form will give you the direction you must travel.

A jar contains 30 black marbles and 15 white marbles. You draw one marble at random. If you draw a black, you win $6. If you draw a white, you lose $11. Find the expected value of this game. $

In Exercises 13-14, find the dimension n of the solution space W of Ax = 0, and then construct an isomorphism between W and R" 1 1 1 1 A = 2 2 2 2 3 3 3 3

Use the like bases property to solve the equation 5ⁿ -=125 n =

Find the distance between the skew lines P(t) = (–4, 3,0) + t (−2, −3, 2) and Q(t) = (−3,−1, 5) + t (1, 3, -1). Hint: Take the cross product of the slope vectors of P and Q to find a vector normal to both of these lines. distance =

Find an equation of the circle that has center (-1, 4) and passes through (5,-2).

Let the subspace V C R³ is given by v={ x₁ x₂ x₃) : x₁+3x₂+2x₃=0} Find a basis of V

Joseph invested $89,000 in an account paying an interest rate of 6.6% compounded how long would it take, to withdrawals are made, quarterly. Assuming no deposits or the nearest tenth of a year, for the value of the account to reach $237,600?

Your employer automatically puts 15 percent of your salary into a 401(k) retirement account at the beginning of each year. The account earns 9% interest (compounded continuously). Suppose you just got the job on January 1st, your starting salary is $35000, and you expect to receive a 3.5% raise at the end of each year. We denote by y(t) the value of your retirement account after t years. Your salary after t years is 35000 1.035. The balance on your retirement account at the beginning is y(0) = 5250. The differential equation modeling this situation is y' = Solving the initial-value problem gives the unique solution y(t) =

Elijah is going to invest in an account paying an interest rate of 5.5% compounded continuously. How much would Elijah need to invest, to the nearest hundred dollars, for the value of the account to reach $1,400 in 16 years?

Charlie reads quickly. He reads 1(3/7) pages every 2/3 minutes. Charlie reads at a constant rate. How many pages does he read per minute? ____________pages per minute

Solve. 3√(x+1) - 2 = 0 Do not include x = in your answer. If there is no solution, the answer is the empty set ø

Find a vector that has the same direction as <-2, 4, 2> but has length 6.

A person invests 10000 dollars in a bank. The bank pays 6.5% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 29500 dollars? A=P(1+r/n)^nt

Solve √2x-5+ √2x = 5 If there are multiple answers, list them separated by a comma. For example 1, 2. If there is no solution, indicate this with the empty set Ø.

Which of the following points are on the graph of y = -2x² - x -8? Select all that apply. A) (14, -414) B) (-13, -333) C) (-8, -128) D) (-4,-35) E) (15,- 473) F) (-12, -283)

Provide a possible/general partial fraction decomposition of the rational expression f(x)/x³(x - 1)(x + 5)⁴(x² + 2x + 9)², where f(x) is a polynomial without common factors and is degree 6.

Express using rational exponents. ∛a² Provide your answer below:

Evaluate each sum. (a) 2+5+8+-+98= (b) 5 - 10/3 + 20/9 - 40/27 + .... =

Caleb bought groceries and paid $1.60 in sales tax. The sales tax rate is 2.5%. What was the price of Caleb's groceries, before tax?

In triangle ABC, m∠A = 38 degrees, m∠C 101 degrees, and the length of AB = 8. Find the measures of the other sides and angles. m∠B = ___________ degrees length of AC= ___________ (Round your answer to three decimal places) length of BC= ______________ (Round your answer to three decimal places)

A person invested $7, 400 in an account growing at a rate allowing the money to double every 6 years. How much money would be in the account after 4 years, to the nearest dollar?

Perform the operation. Give your answer in radical form. You may leave the radicand in exponential form. [(5)^1/2]. [(25)^1/5]

Write out your answer in order of the variable indices to receive full points! 1 0 0 2 -1 0 1 0 1 3 0 0 0 0 0 Write the solution in (a) in a vector form.