Sequences & Series Questions and Answers

Angle α is in quadrant III and angle β is in quadrant IV. If sin α = - and cos β = 1/2, find cos(α + β).

Complete the following sentence so that the resulting statement is true. If a line is horizontal, then its slope is_ If a line is vertical, then its slope is _ If a line is horizontal, then its slope is If a line is vertical, then its slope is

Given that the constant term in the expansion of (3/x - x3/m)4 is -27, make use of the binomial theorem, without expanding, to determine m. The answer is m=

Let f(x) = 5x² - 2 and g(x) = 2x + 2. Find the function or value. a) (f - g)(x) b) (f.g)(x) c) (fog)(4)

The first aircraft has 72 more seats than the second aircraft. The third aircraft has 51 fewer seats than the second aircraft. If their total number of seats is 432, find the number of seats for each aircraft

Find the terminal point P(x, y) on the unit circle determined by the given value of t. t = 5π/2 P(x, y) =

Jam places $10,000 in a bank account that pays 13.5% compounded continuously. After 2 years will he have enough money to buy a car that costs $13,1047 if another bank will pay Jim 14% compounded semiannually, to this a betur deaf? Aher 2 years, Jm will have

Jim places $10,000 in a bank account that pays 13.5% compounded continuously. After 2 years, will he have enough money to buy a car that costs $13,1047 if another bank will pay Jim 14% compounded semiannually, is this a better deal? After 2 years, Jim will have $

A column of 150 PCF concrete containing 60% slag and 45% fly ash and a retarder is to be poured 20 feet deep at a temperature of 60 degrees and a pour rate of 12 feet per hour. What are the Cw and Cc values? A. Cw=1.00 Cc=1.4 B. None of the answers are correct C. Cw=1.00 Cc-1.2 D. Cw-1.20 Cc-1.4

A blimp, suspended in the air at a height of 500 feet, lies directly over a line from a sports stadium to a planetarium If the angle of depression from the blimp to the stadium is 37° and from the blimp to the planetarium is 23°, find the distance between the sports stadium and the planetarium The distance between the sports stadium and the planetarium is feet

Are the following statements true or false? If true, prove the statement. If false, give a counterexample. 1. A matrix Aε Rnxn with n real orthonormal eigenvectors is symmetric. 2. Assume that w =! 0 is an eigenvector for matrices A, B v Rnxn, then AB - BA is not invertible. 3. If the Jordan canonical form of A is J, then that of A² is J².

Evaluate the expression without using a calculator. log 1/100

Find n(A) for the sel A=(700, 701, 702, 7,000) A. n(A)=7,000 B. n(A)=4 C. n(A)=6,301 D. n(A)=6,300

Find the domain of the logarithmic function. f(x) = log (14-x) The domain of f(x) = log (14-x) is (Type your answer in interval notation.)

f is a polynomial function with leading coefficient -10 and degree 30. Describe the end behavior of the graph of f. a) The graph goes up to the left and up to the right. b) The graph goes down to the left and down to the right. c) The graph goes down to the left and up to the right. d) The graph goes up to the left and down to the right.

A person standing close to the edge on top of a 150-foot building throws a baseball vertically upward. The function s(t) = -16t2 +94t +150 models the ball's height, in feet above the ground, t seconds after the ball is thrown. After how many seconds does the ball reach its maximum height? Round to the nearest hundredth of a second.

Simplify (fog)(x) for f(x) = 5x10, g(x) = -4x + 1. Do not enter any spaces in the answer. (fog)(x) =

f(x) = 3x - 2 g(x) = 4x² + 6x – 1 Find the value of (fg)(—3).

In order to purchase a home, a family borrows $101,000 at 3.2% compounded monthly for 15 yrs. What is their monthly payment? Round the answer to the nearest cent CHEE A. $855.68 B. $707.24 C. $906.22 D. $270.27 E $6,877.87

Find the inverse of the function. f(x) =- 3x - 4/ - 8x + 7

A speed boat bought for $13,000 depreciates at 10% per year compounded continuously. What is its value after 7 years? Round the answer to the nearest dollar $6456 $5956 $26179 $6356 none of these

Determine the size of the hole so that the surface of a tank with a horizontal cross section of 1.50 m2 drops at 160 mm/s. The loss over the hole is 3.35 m. CD = 0.63.

Brad decides to purchase a $200,000$200,000 house. He wants to finance the entire balance. He has received an APR of 3.2%3.2% for a 3030-year mortgage. Over the course of the loan, how much interest will Brad pay? Round your answer to the nearest hundredth.

Amir deposits $15,000 at the beginning of each year for 15 years in an account paying 5% compounded annually. He then puts the total amount on deposit in another account paying 9% compounded semiannually for another 12 years. Find the final amount on deposit after the entire 27-year period. The final amount on deposit after the entire 27-year period is

Suppose a 40-year-old person deposits $8,000 per year in an Individual Retirement Account until age 65. Find the total in the account with the following assumption of an interest rate. (Assume quarterly compounding, with payments of $2,000 made at the end of each quarter period) Find the total amount of interest earned.

7) An auditorium has 25 rows. The first row has 10 seats and each row after the first has one more seat than the row before it. Write a rule for the number of seats in the nth row, then find the total number of seats in the auditorium.

did ministrator of a country museum is considering increasing the price of an annual pass by 1% from $50 to $50.50. at the current price, the museum sells 4000 annual passes and the point of elasticity is 0.73. What effect would the increase in price have on the museums annual pass revenue? the total revanue A 1% increase in price by $

The total revenue function for a certain product is given by R = 1060x dollars, and the total cost function for this product is C = 30,000+40x + x² dollars, where x is the number of units of the product that are produced and sold. a. Which function is quadratic, and which is linear? b. Find the profit function for this product from these two functions. c. Is the profit function a linear function, a quadratic function, or neither of these?

Graph the solution set of the following equation: (x + 1)² + (y-2)2 = 9. Label your graph.

A quadratic function is defined by the equation f(x) =-1/2 (x + 5)² - 11. If the range of f(x) is R: {-95.5}, then determine the domain of f(x).

2x-y+z=6 x-3y +z = -2 x + 2y-z = 3 draw a sketch of the three fields and write an explanation about the existence of the SPL solution

Write an equation for the line perpendicular to f(x) = - 2x + 3 and passing through the point (2,0).

By transforming each point on f (x), determine the resulting set of ordered pairs that define g(x) = f (x) - 4. Submit your answer is the form (a,b). Point (-2,5) transforms to: Point (0,4) transforms to: Point (1,-3) transforms to:

Write the equation of the linear function f that satisfies f(-4)= 8 and f(8) = -1.

Is the relation R={(-2, 5), (3, -4), (0, 3), (3, 2), (-4, 3)} a function? Briefly explain why or why not. State the domain of the relation. Use correct notation. State the range of the relation. Use correct notation.

Rewrite the relation 2x-y/3= x - 2 as a function f of x, using function notation. Determine f(-1).

A coin is tossed upward from a balcony. The quadratic function h(t) = − 16t² + 32t + 320 models the coin's height above the ground, h(t), in feet, t seconds after it was thrown. Find the maximum height of the coin.

Determine the solution set of the equation. -4x(2x - 3)2 (5-x)³ = 0 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer.

Find the requested information for the polynomial. 7x²-3x¹ +5x-1 a. The leading coefficient of the polynomial is b. The leading coefficient is c. The degree of the polynomial is d. The parity of the degree is

Select all solutions of the equation. -4x(x-6) (x + 1) = 0

Determine the solution set of the equation. Use correct solution set notation, listing the solutions from smallest to largest separated by a comma. Do not include any blank spaces in your answer. Use / to enter a fraction if needed. (Example: (-1,4,5}) 3x² (4x-3)(1-x)² = 0 Type your answer and submit

Find the requested information for the polynomial. 3x² (4x - 3)(1-x)² a. The leading coefficient of the polynomial is b. The leading coefficient is re... (positive/negative). c. The degree of the polynomial is d. The parity of the degree is

Solve. Round your answers to the nearest tenth if necessary. (5x-6)(3x + 1) = 0 Smaller solution: Bigger solution:

Round your answers to the nearest tenth if necessary. 7x(2x - 7) = 0 Smaller solution: Bigger solution:

For the following function, what is the multiplicity of the zero -9? f(x) = x³ + 9x²-x-9

Solve the following exponential equation. 9x2. 35x = 27 Select the correct choice below and, if necessary, fill in the answer box. A. The solution(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The solution is not a real number.

Write the equation in slope-intercept form, if possible. Enter the equation without spaces. Enter the answer in the form y=mx+b. -9x + 3y = 24

Solve the following logarithmic equation. log 27 1/3 =X Select the correct choice below and, if necessary, fill in the answer box. A. The solution(s) is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) B. The solution is not a real number.

What value makes the expression undefined? x-1/2x

5 year, semi-annual bond, 0.11 coupon, 0.055 YTM. Par is 1000. What should be the price of this bond? A. 1,288.10 B. 1,249.73 C. 1,237.60 D. 1,275.47 E. 1,262.11