Sequences & Series Questions and Answers

A neighborhood carnival has a Ferris wheel with a radius of 30 feet. You measure the time it takes for one revolution to be 70 seconds. What is the linear speed (in feet per second) of this Ferris wheel? What is the angular speed in radians per second?

Find the equation of the quadratic function using the given information. The vertex is (x, y) = (-1, 4) and a point on the graph is (x, y) = (4.8).

This task is relative to the Jo-walking context. Use the variables z and y defined in the text above this question. a. Write a formula that expresses Jo's distance from her car in feet, y, in terms of her distance from her house in feet, z. b. When z = 35, what is the value of y? c. At some moment Jo is 111 feet from her house. What are the values and y at this moment? d. At some moment Jo is 44 feet from her car. What are the values of a and y at this moment?

Solve. √x-6 +8 = x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are B. There is no solution.

Consider the function f(x) = 3 (cos(x − 3) + 1). Determine its amplitude, period, and midline. Enter the exact answers. For the number 7, either choose from the bar at the top or type in Pi (with a capital P).

Find the amount of time it would take for a $38,000 investment to double given the following scenario. An interest rate of 4.56% compounded continuously. Do not round-off anything until you obtain the final answer. Round your answers to the nearest.

The healing time for a broken clavicle is from a Normal distribution with a mean of 41 days and a standard deviation of 6 days. What's the probability a clavicle will heal... 14) in under 50 days? 15) in over 35 days? 16) in between 32 and 44 days?

The local store makes a display of soup that is in the shape of a triangle. There are 20 cans in the Sarow from the top and 68 cans in the 17a. row from the top. a) How many cans are in top row? b) Write a general term for this arithmetic sequence

How many pounds of candy that sells for $0.71 per tb must be mixed with candy that sells for $1.29 per i to obtain 7 b of a misture that should sel for $0.95 per b $0.71-per-b candy $1.29-per-candyb

T(1,0)=(1,4), T(1,1)=(2,5) Remember that T: R^2 -> R^2 is a linear transformation Find: a. T(a,b) b. T(3,5) c. Null(T) d. Range e. Is T onto? Why? f. Is T one-to-one? Why?

How many pounds of candy that sells for $0.71 per lb must be mixed with candy that sells for $1.29 per b to obtain 7 b of a mixture that should sell for $0.95 per b $0.71-per-b candy b $1.29-per-b candyb

What course should the boat follow for its return trip straight back to the marina? Round the answer to one decimal place if necessary. The boat should follow the course A fishing boat leaves a marina and follows a course of S68°W at 8 knots for 15 min. Then the boat changes to a new course of $30°W at 3 knots for 1 hr. Round intermediate steps to four decimal places. (a) How far is the boat from the marina? Round the answer to one decimal place if necessary.

The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. A cylinder contains oxygen at a temperature of 310 degrees K and a pressure of 18 atmospheres in a volume of 120 liters. Find the pressure if the volume is decreased to 105 liters and the temperature is increased to 330 degrees K.

Write the number as the product of a real number and i. - 25

Arrange the steps in correct order to solve the congruence 2x = 7 (mod 17) using the inverse of 2 modulo 17, which is 9. Multiplying both sides of the equation by 9, we get x = 9.7 (mod 17). 9 is an inverse of 2 modulo 17. The given equation is 2x = 7 (mod 17). Since 63 mod 17 = 12, the solutions are all integers congruent to 12 modulo 17, such as 12, 29, and -5.

Employ the regresion function y = a0(1-e¹x) to fit the following data via excel solver. Plot the Solutions.

Determine the amplitude of the function y=- sin x. Graph the function and y = sin x. The amplitude is

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are - 11 and -2.

Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros: 6; - i; -8+ i Let a represent the leading coefficient. The polynomial is f(x)

Determine which of the following sets of vectors are linearly independent in R³. ((-4, 1, 3), (-2,-1, 1), (4, 5, 2)) ((1, 2, 2), (0, -1, 4), (-3, -6, -6)} ((7.2.-1), (3, 0, 5), (0, 4, 4). (-5, 1, 6)) [(0, 1), (1.0), (0, 0))

find the value of the annuity at the end of the indicated number of years. Assume that the interest is compounded with the same frequency as the deposits (Round your answer to the nearest cent.)

The cost of producing x grapefruits is given by C(x)= 450+ 2.4x. Determine the average cost function

The cost of producing x grapefruits is given by C(x) =450+ 2.4x. Determine the average cost function.

Find the cardinal number of each of the following sets. Assume the pattern of elements continues in each part in the order given. a. (214, 215, 216, 217,..., 1013} c. (6, 12, 24, 48, 96, ..., 768} b. (3, 5, 7,..., 101} d. (xlx = k³, k= 1, 2, 3, 83) a. The cardinal number of {214, 215, 216, 217,..., 1013) is b. The cardinal number of (3, 5, 7, 101) is c. The cardinal number of (6, 12, 24, 48, 96,..., 768) is d. The cardinal number of (xix=k³, k= 1, 2, 3,..., 83) is

Larry purchased a new combine that cost $220.500, minus a rebate of $2,500, a trade-in of $8,500, and a down payment of $9,000. He takes out a loan for the balance at 8% APR over 4 years. Find the annual payment. (Simplify your answer completely. Round your answer to the nearest cent.)

Change each of the following equations into general form. x+2)² + (x−1)² = 2 4 a. 1 b. x-5=2(y + 4)²

Write an equation in standard form of the line passing through the points (3, 5) and (-5, 7). The equation is (Type your answer in standard form.)

Solve. 1 12 1 2 25y 25 10y N ▪▪▪ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O B. The solution set is {y I y is a real number and y (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OC. There is no solution.

What if the qualified individual cannot self- administer the aid -in-dying drug ?What assistance is permitted ,if any?

When travelling a fixed distance, the speed at which you travel varies inversely with the time it takes to reach your destination. If it takes 40 minutes when driving at 50 miles per hour, how quickly can you make the trip when driving at 65 miles per hour? Round your answer to the nearest tenth.

Build the least common multiple of A, B, and C using the example/method in module 8 on page 59&60. Then write the prime factorization of the least common multiple of A, B, and C. A = 37³ 13⁹ 19⁹ B = 26 73116. 13. 23 C = 3.52.7.11.17

A point on a line and its slope are given. Find the point-slope form of the equation of the line. P = (1,4); m = 4

Let W be the subspace of R³ spanned by the vectors - 1988 1 P = cijen BALL - WIN W -les seules Find the projection matrix P that projects vectors in 12³ onto W

Jon recently drove to visit his parents who live 90 miles away. On his way there his average speed was 24 miles per hour faster than on his way home the ran into some bad weather). If Jon spent a total of 4 hours driving, find the two rates (in mph). Round your answer to two decimal places, if needed.

Write an equation that expresses the statement. (Use k as the constant of proportionality.) Pvaries inversely as T.

A blue candle and red candle are lit at the same time but burn at different rates. The blue candle is 7.9 inches long when lit and burns at a constant rate of 2.9 inches per hour. The red candle is 5.1 inches long when lit and burns at a constant rate of 1.4 inches per hour. a. For each candle, write a formula expressing the remaining length of the candle (in inches) in terms of the number of hours t since the candle was lit. o Blue Candle: 1 => o Red Candle: One solution: (t, l) 21 ONo solution Infinite number of solutions Preview Preview syntax error b. The time-length relationship for the two candles form a system. Find the solution(s) to this system. syntax error Preview Invalid notation.

Carmen is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges an initial fee of $55 and an additional 70 cents for every mile driven. Company B has no initial fee but charges 80 cents for every mile driven. For what mileages will Company A charge at least as much as Company B? Use m for the number of miles driven, and solve your inequality for m.

A once-popular children's doll is slowly declining in popularity. The quartic function f(x) = 0.002x4 +0.025x³ -0.364x² -7.243x + 86.993, where x is the number of years since 1993, can be used to estimate the number of dolls of this type that were sold (in thousands) during a given year from 1993 to 2003. Estimate how many dolls were sold in 1995.

4. (Systems of equations) Solve the system of equations. Write your answer as an ordered pair. 3x+2y=8 2x-5y=18

First find f+g, f-g, fg and Then determine the domain for each function. g f(x) = 3x + 5, g(x)=x+1 (f+g)(x) = 4x+6 (Simplify your answer.) What is the domain off + g? [0,00) 3 (-∞, - 2) - (- 21.0) (-00,00) (f-g)(x) = 2x+4 (Simplify your answer.) What is the domain of f-g? (-∞0,00) O [0,00) (-2,00) (-∞, -2)U(-2,00) (fg)(x) =

Solve. 1 3 17 1 1 4 4y 6y *** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (y I y is a real number and y (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. The solution(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.). OC. There is no solution.

For f(x)=x² + 6 and g(x)=x²-9, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(4); d. (gof)(4)

Find the domain of the function. f(x) = 63 2 x² - 4x-21

For f(x) = 2x - 4 and g(x) = 4x²-2, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (gof)(2)

Find the average rate of change of the function f(x) = 4x from x₁ = 0 to x₂ = 7.

First find f + g, f- g. fg and — Then determine the domain for each function. f(x) = 4x² - 15x -54, g(x)=x-6 (f+g)(x) = 4x² - 14x-60 (Simplify your answer.) What is the domain of f + g? 30 (-00,00) (-∞, -30) (-370,00) 00, 7 O [0,00) (f- g)(x) = (Simplify your answer.)

For f(x)=x² +6 and g(x)=x²-9, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(4); d. (gof)(4) a. (fog)(x) = x4-18x² +87 (Simplify your answer.) b. (gof)(x)= x + 12x² +27 (Simplify your answer.) c. (fog)(4) =

2. For each expression, write an equivalent expression by applying the distributive property. Part a: (x+2) (x +9) Part b: (x – 5)² = "$4 Optional: You can use the rectangular diagram below to help you find the equivalent expression. & 9972

For f(x) = x + 3 and g(x) = 5x + 4, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(1); d. (gof)(1) a. (fog)(x) = 5x +7 (Simplify your answer.) b. (gof)(x) = 5x + 19 (Simplify your answer.) c. (fog)(1) = 12 d. (gof)(1) =

A child is pulling a wagon with a force of 40 pounds. How much work is done in moving the wagon 60 feet if the handle makes an angle of 35° with the ground? Round to the nearest foot- pound.