Sequences & Series Questions and Answers

A can is in the shape of a right circular cylinder. The circumference of the base of the can is 12 inches, and the height of the can is 5 inches. A spiral strip is painted on the can in such a way that it winds at the can exactly once as it reaches from the to the top. It reaches the top of the can directly above the spot where it left the bottom. What is the length, in inches, of the strip? (A) 17 (B) 13 (C) 25π (D) 12π (E) 60

A person walks 4 km north, 1 km east, 4 km north, and then 5 km east. "As the crow flies," how far is the person from the starting point?

Evaluate the piecewise defined function at the indicated values. f(x)={4 if x ≤ 2 2x-5 if x >2 f(-3) = ? f(0) =? f(2)=? f(3)=? f(5)=?

The population of a town of 32, 000 people is expected to grow exponentially at a rate of 1.7% per year. Estimate the population in 4 years' time. Round to nearest whole number.

Riley works at a coffee shop, where an 8-oz cup of coffee costs $3, a 15-oz cup costs $4, and a 20-oz cup costs $5. During one busy period, Riley served 30 cups of coffee, using 500 ounces of coffee, while collecting a total of $132. a. Setup the system of equations that can be used to determine the number of cups of each size Riley filled. b. Write the augmented matrix that corresponds to the system of equations from part a. c. Solve the system of equations. How many cups of each size did Riley fill?

Giving that X₁.X₂..., X are N random variable with expectation value X₁X₂...XN, respectively. Assuming that fx₁x₂....xn(x₁ x₂ .....xn is the joint density function of N random variables. Find the expectation of new random variable, X given by X = g(X₁, X₂,.....XN) = Σ a₁x₁ Hint: you can use concept of marginal probability of k-dimensional RVs with k = 1.

Q4) The table shows various values of functions f(x), g(x), and h(x). x -1 0 1 2 3 4 f(x) 7 -2 0 2 4 1 g(x) -3 -4 -5 0 1 1 h(x) 0 4 1 1 5 5 Use the table to evaluate the following values: a. (f+h)(3) b. (f-g)(0) c. (f. h)(-1) d. (g/f)(2) e. (g/h)(-1) f. (h/f)(4)

Find the third-order Fourier approximation to the function f(x) = x² on the interval [0,2π].

Complete the following conversions. 1) 500 cm² = m² 2) 1400 ft²= yd² 3) 2.8 yd² = ft² 4) 564 m² = km² 5) 2700 cm² = m² 6) 320 cm² = mm² 7) 435,000 mm²= cm² Choose an appropriate metric unit to measure the following. 8) the surface area of the Great Salt Lake: mm², cm², m², or km² 9) the surface area of a contact lens: mm², m², or km² 10) the area of a football field: mm², cm², m², or km²

Determine a simplified equivalent expression for each using the co function identities. a) sin 5π/4 b) cos π/3 c) tan 5π/3

Solve In x = -0.69 for x. Round to the nearest hundredth as needed. Provide your answer below:

Find the domain of the function. f(x)=√(5x-45) The domain is ____. (Type your answer in interval notation.)

xy" (x+1)y' + y =0 with a particular solution y(x) = ex is given.

Find the number of terms in the arithmetic sequence. {5, 12, 19, ..., 327}

Use algebra to show that pk+1(n) − Pk+1(n − 1) = Pk(n). Note do not expand Pk+1(n), Pk+1(n-1), and pr(n) have a lot of common factors.

Determine whether the following sequence is arithmetic. If so, find the common difference. (Hint: If it is not an arithmetic sequence, type "N/A" in the box for the common difference.) {4, 6, 9, 13, ...} The sequence____The common ratio is type your answer...

(a) Find the three-digit number that increases by 30% when each of its digits are increased by 1. (b) Show that no three-digit number increases by 40% when each of its digits are increased by 1.

8. What is an equivalent trigonometric ratio using c̲o̲s̲i̲n̲e̲ for sin 7π/16?

Describe the transformations from the graph of f(x)=3√x to the graph of g(x) below. Then graph the function showing at least 3 exact points. g(x) = (-1/2 )(1√x+1-3)

Numerical solution of ordinary differential equations: Consider the ordinary differential equation: dy/dx = -2x - y, with the initial condition y(0) = 1.15573. Solve the given equation analytically, and plot the results.

Bob says that the domain of a square root function will always be only {xlx ≥ 0}, but Sally disagrees and says she can prove it graphically. Provide a graph and equation that justifies Sally's response and describe the domain of that graph.

Bill has $12,400 in a regular savings account earning 4 2/3% annual interest that is compounded monthly. How much will be in the account at the end of 3 years? Round to the nearest cent, and do not include the dollar sign in your answer.

If A in the following options represents area then which of the following is odd ? a) c²=a² + b² - 2abcos8 b) A = absinθ c)sinA/a=sinb/b=sin C/c d) A = 1/2absinθ

Evaluate log₁ /₂(3/5) using the change of base formula. Round to the nearest hundredth as needed. Provide your answer below:

Which of these is an equivalent trigonometric ration for sin 2π/5 a) cos(π/10) b) sin(3π/5) c) -cos(9π/10) d) All of the above

Explain why the equation cos²x = 3/4 has solutions in all four quadrants. List all those solutions.

A new MP3 player was purchased for 320 and in 1 year it was selling used online for 210. If the value continues to decrease exponentially at this rate, determine the value of the MP3 player 3 years after it was purchased. Round to the nearest cent.

Evaluate ∫∫∫8ydV where E is the region between x+y+z=6 and x+y+z=10 in E front of the triangle in the yz-plane with vertices, in (y,z) form: (0,0), (1,2) and (1,4).

If the ant colony's population can be modeled by the function, f(x)=(2.5x)+(64), how many ants would you expect to be in the colony after 56 days? 2.5 (56) + 64 140 + 64 ? A.)204 ants B.)216 ants

Given g(p) =p-2 and h (p) =p³ +4p²-2. What is g(p). h (p)? a) p⁴+2p³ - 8p²-2p+4 b) p⁴+6p³ - 8p²-2p+4 c) p⁴ + 2p³ - 8p²-2p - 4 d) p⁴ + 6p³ - 8p²-2p - 4

Determine the solution for 8+ 2 cot x = 12 in the intervals of 0 ≤ x ≤ 90° a. 26.6⁰ b. 63.6⁰ c. 0.6⁰ d. 38.4⁰

You have the functions f(x) = 3x + 1 and g(x) = |x– 1| i) Let h(x) = f(x)g(x). Explain why the Product Rule can be used to compute h`(0) but cannot be used to compute h`(1). Then, compute h`(0). (What are the theorem's hypotheses? Why do they apply?)

Which of the following is NOT a solution to the equation 4 sin²x - 1 for 0 ≤x ≤ 2π? a. 30° b. 210⁰ c. 150⁰ d. 120°

Use the function f(x) = -5.2x + $460, which estimates your monthly gas bill given the average temperature, to answer the following questions. How much would you expect to pay if the average temperature for the month was 28° F? A) 314.40 B) 605.60

Solve the equation. 4x-8= 12 + 6x x =

With specific examples and detail from the documentary, Flow, explain whether fresh water should be considered a commodity or should access to water be declared a fundamental human right?

If an airplane travels at an average speed of 510 mph, how far does the airplane move in 50 minutes? a) 400 miles c) 500 miles c) 425 miles d) 475 miles

There is a drawing at work for some Sam Smith tickets. There are 15 people that would like to receive tickets for the concert, but there are only 4 tickets. If you are someone that would like a ticket, what is the probability that you will be chosen?

What is the sample space for a 6-sided die? What is the size of the sample space? If you roll the die, what is the probability that you will land on a 4? 4. If you roll the die, what is the probability that you will land on a number less than 5?

A wooden bowl artifact carved from oak was found to contain 55% of the carbon-14 normally found in oak. Given that carbon-14 has a half-life of 5, 730 years, estimate the age of the bowl

In 2005, Capital City determined its population, in millions, could be expressed by this function: P(x) = (-.05x )+ (53.7) where x is the number of years after 2005. Which of the following statements is true? The city's population was 53.45 million in 2005. The city's population was 54 million in 2011. The city's population is increasing at a rate of .05 million each year. The city's population is decreasing at a rate of .05 million each year.

Find the surface area of a sphere with a radius of 1.5 ft. Use 3.14 for π. (Use SA=4πr², but 3.14 for π) a) 9.42 ft^2 b)18.84 ft^2 c) 84.78 ft^2

Let f(x) = 7x² - 5x+3 and g(x) = 2x² + 4x - 6. What is the value of g(x) - f(x)? a) -5x²-x-3 b) -5x² +9x-3 c) -5x²-x-9 d) -5x² +9x-9

State the property (or properties) of equations that can be used to solve the following equation, then use the property (or properties) to solve the equation. 3x + 25 - 11 Which of the following properties can be used to solve the equation? A) substitution property and division property B) subtraction property and addition property C) subtraction property and division property D) division property and multiplication property

By use PDE thought, If it takes a 2 cm long insulated bar 7 minutes to cool down to room temperature, how long does it takes a 6 cm bar (made of the same material)? Explain.

You are using the numbers 1-8 to create a 5 digit code. Each number can only be used once. How many different codes are possible? (order matters because 12345 is a different code than 54321, and repetition is not allowed because you are only allowed to use each number once.) Show your work.

On January 1, you invest $1550 into an investment account. On April 1, you withdrew $ 720. On June 1, you invested $2260. On November 1, you invested $730. Determine the average monthly balance in the investment account.

1)During the summer Mary could buy 15 cooling units for $3300. How much will Mary have to spend in order to buy 39 cooling units for her tenement houses? 2). John averaged 114 miles on the first 2 days of his trip. He averaged only 93 miles on the other 5 days of his trip. What was the overall average number of miles traveled per day?

For the given algebraic expression, give the coefficient of each term and give the constant term. 2x⁴ +6x³-7

How can knowing the mathematics of ratios and percents be used to help make decisions when shopping?