Sequences & Series Questions and Answers

Let G be an abelian group acting on a set X. Suppose that there is only one orbit under this action. Assume that G||X|. Prove that there exists e≠g ε G such that Fix(g) = X.

Find a power series for the function, centered at c. F(x) = 4/3-x, c=1 Determine the interval of convergence. (Enter your answer using interval notation.)

To find the distance AB across a river, a distance BC= 358 meters is measured off on one side of the river. It is found that ß= 113°20' and that y = 17°20'. Find the distance AB.

(3) Given below is the graph of f(r). Note the graph is not drawn to scale. (a) List the real zero(s) of f(x). (b) Assuming all of the zeros are real, what is a reasonable factored equation for f(x)?

A cruise ship maintains a speed of 14 knots (nautical miles per hour) sailing from San Juan to Barbados, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan at a direction of 19° off a direct heading to Barbados. The captain maintains the 14-knot speed for 15 hours, after which time the path to Barbados becomes clear of storms. (a) Through what angle should the captain turn to head directly to Barbados? (b) Once the turn is made, how long will it be before the ship reaches Barbados if the same 14-knot speed is maintained? (a) The captain should head through an angle of 28.7°. (Do not round until the final answer. Then round to one decimal place as needed.) (b) The time it will take for the ship to reach Barbados is 29.1¹ hours. (Do not round until the final answer. Then round to one decimal place as needed.)

Subtract. 8/(x + 4 )- 8/X Select the correct choice below and fill in any answer boxes within your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) a)8/(x + 4 )- 8/X=___x≠__ b)8/(x + 4 )- 8/X==___no numbers must be excluded

Give the equation of the surface obtained by rotating the plane curve 5x²-6xy + 5y²-32 = 0 Around the line z=0, x-y=0

The angle of elevation to the top of a tall building is found to be 15° from the ground at a distance of 0.8 mile from the base of the building. Using this information, find the height of the building. The buildings height is ____ feet. Report answer accurate to 2 decimal places.

Evaluate the function at the given values of 7x²-1/x² a) f(2) b)f(-2) c) f(-x)

Begin with rewriting the given equation in general form. -x² + 7x = 12 -x² + 7x- ____ = 0 (-1)(-x²+7x- ___)=(-1)0 x²-___x + 12 = 0

Consider the following points. (−1, 7), (0, 0), (1, 1), (4, 58) (a) Write the augmented matrix that can be used to determine the polynomial function of least degree whose graph passes through the given points.

The equation of a parabola is y=x²-10x+26. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions.

Use the graph of a function y) to fod the absolute mamums and the absolute minimam, if they exist identify any local maximum values or local minimum values

Subtract as indicated. (7x-33)/(x-5) -( x-3)/(x-5) Select the correct choice below and fill in the answer box(es) to complete your choice. A).(7x-33)/(x-5) -( x-3)/(x-5)=_____no numbers must be excluded. b)(7x-33)/(x-5) -( x-3)/(x-5)=______,x≠_____

In 1991, the life expectancy of males in a certain country was 66.9 years. In 1996, it was 70.5 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991. The linear function E(t) that fits the data is E(t)=___t+____ Use the function to predict the life expectancy of males in 2007. E(16)=___

Let p be an odd prime number. Show that p-1 Σ(k-1)!(p-k)!k-1=0 mod p. k=1

If (x-1) is a factor of p(x), then a) p(-1) = 0 b) p(0) = 1 c) p(1) = 0 d) p(0) = -1

Which sets of ordered pairs represent functions from A to B? A = {3, 4, 5, 6} and B = {-2, -1, 0, 1, 2} a) {(3, 1), (4, -2), (5, 0), (6,2)} b) {(3, 2), (6, 0), (4, 1)} c) {(3, 0), (4, 0), (5, 0), (6, 0)}

Healthy cardio exercise typically raises a young person's heart rate to 150 bpm. Your team monitored a patient's heart rate during an exercise stress test, obtaining the following data. Heart Rate Time (s) 0:00 62 bpm 0:10 66 bpm 0:20 69 bpm 0:30 71 bpm 0:40 78 bpm 0:50 82 bpm 1:00 87 bpm When will the patient's heart rate reach the target 150 bpm?

Find the solution to the linear system of differential equations {x'=-x-4y y'== 2x + 5y x(0) = 8) and y(0) = -5 x(t) = 8e^(31)-6e^(t) y(t) = -8e^(3t)+3e^t

Add as indicated. {(8x +4)/(3x + 2 )+ (x + 2 )/(3x+2)} Select the correct choice below and fill in the answer box(es) to complete your choice.(Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) A.) {(8x + 4 )/ (3x + 2 )+ (x + 2 )/(3x+2)}=__,x ≠__ B.) {(8x + 4 )/ (3x + 2 )+ (x + 2 )/(3x+2)}=______ no numbers must be excluded.

Solve the problem. Assume all data are accurate to two significant digits unless greater accuracy is given. Two pieces of equipment were purchased for a total of $7000. If one piece cost $330 more than the other, find the price of the less expensive piece of equipment. A)$3300 B)$3665 C)$3335 D)$3700

Use the given table of an exponential function to answer the following questions. X f(x) 0 5 1 4.2 2 3.528 3 2.9635 a) Is the function, represented in the table, increasing or decreasing? Circle one. b) Calculate the growth or decay factor below. c) State the ordered pair for vertical intercept of f(x), if possible otherwise right N/A. d) Write the equation of the exponential function given by f(x).

Determine the parametric equations of the line through P(1, 7, -2) and Q(-3, 6, 8). x(t) = _____ y(t) = _____ z(t) = _____

Explain in your own words how to find the slope of a line. Find the slope of the line that has intercepts at the points (0,-2) and (3,0).

DHS Corp has announced that its net income for the year ended June 30, 2017, is $1,824.21 Corp had an EBITDA of $5,174,366, and its depreciation and amortization expense was equa $1,241,790. The company's average tax rate is 34 percent. What is the amount of interest c for the firm? $1,187,720 $939.747 $2,763.961 $1.168,615

Find the indicated terms of the arithmetic sequence with the given description. The twelfth term is 126, and the eighth term is 150. Find the first term and the nth term. a₁=? aₙ=?

Evaluate the following expressions. Write the exact value or round to four decimal places if necessary. cosh (0) = coth (1) = csch ( 2 ) = sinh ( 3 ) = sinh ( In ( 3 ) ) =

Complete the polar form of 5 - 5i√3. Simplify all radicals and fractions. Express the argument θ in radians, with 0 ≤ θ < 2π ___ ( cos____+ i sin ____)

Two northern towns are at record low temperatures. One is at -13° and the other is at -22°. What is the difference between the temperatures in the towns?

Let p be prime. Using Fermat's little theorem, prove that n: 2ᵖ-² +2 x 5ᵖ-² +10ᵖ-² - 1 is a multiple of p if and only if p ≠ 2,5. [Hint: for p ≠ 2,5, consider 10n.]

Use the imaginary number i to rewrite the expression below as a complex number. Simplify all radicals. -√-99

When 6x²-x-7 is divided by x+a, the remainder is 5. Determine the value of a. a) a=-1/2 or a=2/3 b. a=1/3 or a=-2/3 c. a=1/2 or a=-4/3 d. a=-3/2 or a=4/3

Using sigma notation, write the following expression as an infinite series: 1+ 3/4 + 9/16+ 27/64+..... A Σn=0 n²+1/n² B Σn=0 n²+1/n² C Σn=0 1(3/4)n D Σn=0 1(3/4)n

You owe $100 on a credit card. You purchase $45 worth of groceries and then make an $80 payment. What is your balance now?

What is the monthly payment on a 30-year mortgage of $200,000 at 8% interest per year, compounded monthly? (Round your answer to the nearest cent.) $ _______ What is the total amount paid on this loan over the 30-year period? (Round your answer to the nearest cent.) $ _______

Duffln House, which is now the largest publisher of books sold at the OHaganBooks.com site, prints three kinds of books: paperback, quality paperback, and hardcover. The amounts of paper, ink, and time on the presses required for each kind of book are given in this table. Paperback Quality Hardcover Total Paperback Available Paper (pounds) 3 2 1 6,000 Ink (gallons) 2 1 3 6,000 Time (minutes) 10 10 10 30,000 Profit ($) 1 2 3 The table also lists the total amounts of paper, ink, and time available in a given day and the profits made on each kind of book. How many of each kind of book should Duffln print to maximize profit? Paperback ____________ books Quality Paperback __________________ books Hardcover _________________ books

The function x(t) solves the differential equation x"+ xx' = 0. Determine the initial conditions for which x(t) diverges at some finite t > 0. a) x(0) = 1, x'(0) = -1 b) x(0) = 5,x'(0) = 0 c) x(0) = 2, x'(0) = -2 d) x(0) = 0, x'(0) = 2 e) x(0) = -2, x'(0) = 2

The bacteria population in Colony A grows according to the recursive formula. The table shows the bacteria population of Colony B at different points in time. The initial population for Colony B is less than the population of Colony A. Will Colony B always be the smaller colony? Justify your reasoning. a₁ = 20000 aₙ = 1.1aₙ-₁ Time Colony B Initial 1000 After 1 hour 1200 After 2 hours 1440 After 3 hours 1728

Find a particular solution to the differential equation using the Method of Undetermined Coefficients. d²y/dx² -3(dy/dx)+7y=xeˣ A solution is yₚ(x) =

Write an equation for the transformed logarithm shown below, that passes through (2,0) and (-1,3)

Express as a single logarithm and simplify log₅0-log₅0.4 a) log₅20 b) log₅49.6 c) 2 d) 3

Illustrate the Cauchy Schwarz Inequality using the vectors A = (2, 0, -1), B = (0, 1, -1).

A painting was purchased for $10 000 in 2000. The painting increased in value by 1.2% per year. Find the anticipated value of the painting in 2020. a) $54 735.66 b) $96 462.93 c) $12 694.34 d) $11 959.35

Your parents invested money in college savings accounts when you and your sister were born. The balance A (in dollars) of your account after f years can be modeled by A = 3400e^0.071 principal? Which has a greater balance after 10 years? The graph shows the balance of your sister's account over time. Which account has a greater Your sister's account has a greater principal; Your sister's account has a greater balance after 10 years. Your sister's account has a greater principal; Your account has a greater balance after 10 years. Your account has a greater principal; Your sister's account has a greater balance after 10 years. Your account has a greater principal; Your account has a greater balance after 10 years.

Let V be a vector space and S = {(2, -1, 3), (1, 2, 1)). Show at least one basis of V = R^3.

Write the word phrase below as an algebraic expression, using b as the variable. thirteen times a number The translation is__________

Rule 1: If K outcomes can occur during each of N trials of an experiment, then kⁿ different sequences can result. Rule 2: If K1 outcomes can occur during a trial of one experiment, and K2 outcomes can occur during a trial of another experiment, then K1K2 different sequences can result. Rule 3: The number of ways that N objects can be arranged in order is N!. Rule 4: The number of ways of selecting r objects from N objects when order matters is N!/(N-r)! Rule 5: The number of ways of selecting r objects from N objects when order doesn't matter is N!(N-r)!r!. Show your work. 1. Using Rule 1 You have 64 people who are running for office. You flip the coin. How many times do you flip the coin so each person has a sequences number? 2. What if there are 128 people? 3. If 60 people decide to run for vice president and you use a die, How many colors need to be on the spinner so each person has their own color and number. Show your work. 4. How about 48 people?

The value of a new car depreciates at a rate of 8% per year. Write an equation to represent the approximate value, V, of a car purchased for $42 000, after n years. a) $42 000(0.92)^-n b) $42 000(1.08)^n c) $42 000(0.92)^n d) $42 000(1.08)^-n

Use the intercepts to graph the equation. 5x - 15=3y Use the graphing tool to graph the line. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.