Sequences & Series Questions and Answers

The height of a radio tower is 700 feet, and the ground on one side of the tower slopes upward at an angle of 10°. (a) How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 150 feet from the base of the tower? (b) How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 150 feet from the base on the flat side?

Revenues of software publishers in a country for the years 2009-2016 can be modeled by the function S(x)=92.482 e 005205x where x-9 represents 2009, x= 10 represents 2010, and so on and S(x) is in billions of dollars. Approximate, to the nearest unit, revenue for 2016

Solve triangle ABC, (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a=67, c=51, C=53"

(a) The following statement is either True or False. If the statement is true, provide a proof. If false, construct a specific counterexample to show that the statement is not always true. Let H and K be subspaces of a vector space V, then HUK is a subspace of V.

Solve. If there is more than one solution, separate them with a comma. If there are no solutions, enter DNE. -3-4|6x + 9| = - 35

If f(n)= -3n+2, what is the value of f(12)? f(n) = -3n+2 f(12) = -3(12) + 2 f(12) = ? + 2 f(12) = ? A. 38 B. -38 C. -34

The graph showing the total number of prisoners in state and federal prisons for the years 1960 through 2009 is shown in the figure. There were 212,458 prisoners in 1960 and 1,609,905 in 2009. Answer a through d. a. What is the average rate of growth of the prison population from 1960 to 2009? The average rate of growth of the prison population from 1960 to 2009 is 28519 per year. (Round to the nearest integer as needed.) b. What is the slope of the line connecting the points satisfying conditions above? The slope of the line connecting the points satisfying the conditions above is 28519 per year. c. Write the equation of the secant line joining these two points on the curve. The equation of the secant line connecting the two points (1960,212458) and (2009,1609905) is (Type an equation. Type your answer in slope-intercept form. Use integers or decimals for any numbers in the equation.)

Someone measured two sides of the rectangle shown below, and they used a strange unit of measurement: We want to know the total area of this rectangle in units of lans². Below are some unit conversion facts involving these strange units. Which fact(s) below will we need to use? [Select only the one(s) we actually need for the conversion. 19 teeps 3 mibs 3.5 urts = 4 lans 6 hars= 6.5 lans 2 urts = 9.5 flots 5 teeps 5.5 hars

graph the solution set of the system of inequalities Graph the solution set of the system of inequalities x ≥0 y ≤ 0 3x + 4y > 12

Describe the long run behavior of f(t) = -4(1/4)ᵗ +4 As t→∞, f(t) → ? As t→∞, f(t) → ?

Consider the points (1, 4), (3, 6), (5, 4). (A) Write down an inconsistent system for finding a and b such that y = ax + b passes through all 3 points. (B) Write down a consistent system for finding a and b such that y = ax + b is the least squares best fit for the points. For both (A) and (B), set up, but don't solve the relevant systems of equations.

The table displays the scores of students on a recent exam. Find the mean of the scores to the nearest 10th. Score Number of Students 70 1 75 4 80 7 85 2 90 8

Determine the geometric mean of the following five terms 2.5, 4 1/4, 7.15, 11 3/5, 15.

A person places $7420 in an investment account earning an annual rate of 5.9%, compounded continuously. Using the formula V = Peʳᵗ where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years.

The physician orders 1000 ml of 5% dextrose in water to infuse at 40gmt/min. How many hours must the IV infuse? (20 g/ml ser)

The Supreme Court ruling in Marbury v. Madison did which of the following? (a) Recognized judicial review. (b) Increased the powers of Congress. (c) Increased the power of the president. (d) Caused conflicts between the states and the federal government.

Compute the arc length of the parabola x = y² and the line x = by from (0,0) to (b², b) for b > 0. What happens as b increases?

Use a table to solve each equation. Round to the nearest hundredth. 27. 2x+3 = 512 28. 3x-1 = 72 29. 62x = 10 30.52x = 56

A city's population is 12,800. It is predicted that the population will increase by 3% each year. Part a: Write a function that can be used to find the city's population after t years. Part b: If the city's population, p, continues to grow 3% per year, what will the approximate population be in 15 years.

You are considering renting a car from two different rental companies. Proxy car rental company charges. $0.32 per mile plus an $18 surcharge. YourPal rental company charges $0.36 per mile plus a $12 surcharge. (a) Write a function that shows the cost of renting a car from Proxy. (b) Write a function that shows the cost of renting a car from YourPal. (c) Which company offers the better deal for an 820-mile trip? Give a mathematical reason for your answer. (d) For what distance is the price the same for both companies? Give a mathematical reason for your answer.

Solve and check the linear equation. (x + 7)/12 = 1/6 + (x -2)/7 What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (A) The solution set is { __ }. (Simplify your answer. Type an integer or a fraction.) (B) The solution set is {x | x is a real number}. (C) The solution set is Ø.

Solve and check the linear equation. 28-x/2=x/5 What is the solution? A. The solution set is B. The solution set is {x|x is a real number}. C. The solution set is Ø.

Someone measured the length of the line segment below, and they used a strange unit of measurement: rets Here are some facts about this unit (and some other strange units): 8 teeps 3 kads 2.5 quors = 8.5 nems 9 hars = 6 quors 7.5 rets = 4 kads 7 nems = 3.5 rets Suppose we want to determine the length of this line segment in units of teeps. Which conversion fact(s) will we need to use? [Select only the one(s) we actually need for the conversion.]

1. y varies directly with x a. If y = 6 when x = 2, find x when y = 12. Show your work. b. If y = 25 when x = 15, find y when x = 6. Show your work.

Find the constant of variation. Write in fraction form (a/b) when applicable. X y 27 9 30 10 60 20

Suppose that your favorite restaurant delivery service is offering a deal when you order in bulk: Get 3 burritos from Burrito-Boss for $12.05. Each additional burrito costs $4.85. Let b represent the total number of burritos you order, and let C represent the total cost in dollars. Complete the table of values below: Do not use any dollar signs in your answers. b (burritos) C (dollars) 3 4 5 6 b

2. a. Determine the domain and range of the relation. Write answers as inequality statements. b. Is the relation a function? Give a reason for your answer. 3. You are considering renting a car from two different rental companies. Proxy car rental company charges. $0.32 per mile plus an $18 Relations a. Write a function that shows the cost of renting a car from Proxy. b. Write a function that shows the cost of renting a car from Your Pal. c. Which company offers the better deal for an 820-mile trip? Give a mathematical reason for your answer. d. For what distance is the price the same for both companies? Give a mathematical reason for your answer. Maximum file size: 50 MB, maximum number of files:

Identify the constant of variation. 6y - 7x = 0 The constant of variation is k = ____. (Type an integer or a fraction.)

Find the constant of variation. Leave in fraction form (a/b) when applicable. y = 6x

Write the equation in slope-intercept form. Then find the slope and y-intercept of the line. y = -1 Write the equation in slope-intercept form. ____ (Type an equation. Type your answer in slope-intercept form.)

Use your graphing utility to enter each side of the equation separately under y₁ and y₂. Then use the utility's TABLE or GRAPH feature to solve the equation. 2x + 2(x5)= 3x - 7 Use the TABLE feature to display a table of values. Examine the table on your graphing utility and use these values to complete the table below.

A person made a table for an equation on their calculator, and this is what it showed: X y 2 5 5 3 8 9 11 -1 14 13 If possible, find the following settings they used on their calculator. What is ∆TBL? We can't easily tell from the given information

The equation d = 4-1/15 f represents your distance d from home for each minute t you walk. a. If you graphed this equation, what would the slope represent in context? Explain your answer. b. What would the constant term 4 represent? c. Are you walking towards or away from home?

-3x + 2y = 6 Find the intercepts. Show your work.

A bank loaned out $24,500, part of it at the rate of 14% annual interest, and the rest at 15% annual interest. The total interest earned for both loans was $3,545.00. How much was loaned at each rate? $ was loaned at 14% and $ was loaned at 15%.

Obtain the Taylor series solution of the initial value problem y' = 1-2ty, y(0) = 0 with h=0.1 and p=2.

Integrate the function f over the given region. f(x, y)=x/3+y/4 over the trapezoidal region bounded by the x-axis, y-axis, line x = 3, and line y=-4/3x+8 46 18 30 22

The mean IQ score for 1500 students is 95, with a standard deviation of 10. Assuming the scores have a normal curve, answer the following. a. How many have an IQ score between 85 and 105? b. How many have an IQ score between 75 and 115? c. How many have an IQ score over 125? a. The number of students with an IQ score between 85 and 105 is __. (Round to the nearest person as needed.) b. The number of students with an IQ score between 75 and 115 is __. (Round to the nearest person as needed.) c. The number of students with an IQ score over 125 is __. (Round to the nearest person as needed.)

Find the partial sum Sn of the arithmetic sequence that satisfies the given conditions. a 5, d = 5, n = 20 S20=___

Write the expression as an algebraic expression in x for x > 0. 5 tan(arccos x)

Let u and v be two vectors in an inner product space so that ||u|| = 2, ||v||| = 3 and the angle between the two vectors is 30°. Find the angle between vector u + 5v and vector u - 6v.

Jerome wants to invest $20,000 as part of his retirement plan. He can invest the money at 5.1% simple interest for 32 yr, or he can invest at 3.7% interest compounded continuously for 32 yr. Which investment plan results in more total interest? 3.7% interest compounded continuously 5.1% simple interest

Use the equation of the polynomial function f(x)=-3x³-x to complete the following. (a) State the degree and the leading coefficient. (b) Describe the end behavior of the graph of the function. (c) Support your answer by graphing the function.

Use the given graph of the polynomial function to complete the following (a) Estimate the x-intercept(s) (b) State whether the leading coefficient is positive or negative. (c) Determine whether the polynomial function is cubic or quartic.

Which of the following sequences is an arithmetic sequence? Select all correct answers. Select all that apply: -4, 1,6, 1.-4.... 2.7, 12, 17, 22,... -6.-11,-16, -21.-26,... 1,-1,-5,-7.-11.... -3, -6.-9, -6, -3....

How many terms are there in the following finite arithmetic sequence? 24, 28, 32,..., 80

Solve for the missing sides and angles of ΔABC if A = 40°, a = 22, and b = 25. Round the measures of the unknown angles and sides to 1 decimal place.

Find all x-values that satisfy the equation cos (2x) - 2 sin(2x)cos (2x) = 0,0≤x≤ 2π. Give the exact answers (no approximation).

Find the exact values of sin 2θ, cos 2θ, and tan 2θ for the given value of θ. 180° <θ < 270° cot θ = 4/3 sin 2θ = cos 2θ = tan 2θ =

Continuous Compound Interest Formula Continue watching the intro video and complete the following: If P dollars are invested for t years at annual interest rate r, compounded _ _ then the future value S is given by dollars. (Memorize) Ex: If $1000 is invested at 5% interest, compounded continuously for 7 years, what is the future value of the investment?