Sequences & Series Questions and Answers

Many beach regulators use the geometric mean of the bacteria concentrations at individual beaches to determine when the water is unsafe for swimmers. Suppose a sample of five beaches had the following bacteria readings: 10, 148, 250, 995, 502 Find the geometric mean. 179 1,503 7,517 201

Question (3): Let g(x) = 3-*, x = [1/3,1]. (a) Show that g(x) satisfies the Fixed Point Theorem. (b) Find n such that |P-P| < 10-3 where P is the fixed point of g(x).

The Co. XYZ manufactures a product and sells it for $8 a unit. Its fixed costs are $5.000 and its Variable cost per unit is given by the equation. Calculate the amount q of total balance cost 2, 444 (X) = 2200

Let f(x) = 3√x + 1 and g(x) = x³ − 3. a) Find the value of g (f (7)). b) Find (g(f(x)).

Multiple Choice: The optimal soil pH for growing corn is approximately 6.4. Find the optimal hydrogen ion concentration of the soil. Recall: pH =-log[H+] (a) -0.8062 moles per liter (c) 0.8062 moles per liter (b) 10-6.4 moles per liter (d) 106.4 moles per liter

Jack estimates he will need $25,000 to startup a coffee stand. If he has $10,000 to invest in a savings plan that earns 3% interest compounded monthly, how long will it take to reach the $25,000 he needs to start his business? Setup an equation and solve. Label your answer and round to one decimal place.

Assume that all variables represent positive real numbers. 6 7 √x38 Leading coefficient: Leading variable: Power on leading variable: Index value: Radicand variable: Power on radicand variable:

In ΔFGH, f= 93 inches, h = 89 inches and ∠H=72°. Find all possible values of ∠F, to the nearest degree.

Compare and contrast the following in details: a. An arithmetic sequence and a geometric sequence. b. A sequence and a series. c. Discrete data and continuous data. d. An explicit and a recursive representation.

Find the inverse of h(x). Then graph the inverse. h(x) = -x³ +2

Evaluate if possible. Round to the nearest thousandth. (-32) -3/5

Evaluate the radical. Y√1 if y ≥ 2

Evaluate each expression to four decimal places. 13. e5 15. e -4 14. e 3/2

Graph each function. Then find the domain, range, and y-intercept. 4. y = -4(2)x 5. y = 1/4(10) x 6. y = 8(0.25)x

A sum or difference function with at least one local maximum or minimum. The two functions you must add Trigonometric function: y=0.5sin x + 1.4 Polynomial Function: y=x^3 - 10 State the Local Max and Local Min. Justify your answer with reference to the graph of this function and the sign of IRC. Provide a sketch of your function.

Evaluate the following expression, using a calculator if necessary. If the answer does not exist, indicate "DNE." cos-¹(-0.5)

Rewrite sin80 in terms of the appropriate cofunction.

Evaluate the expression, using a calculator if necessary. Round your answer to four decimal places. sin 102

Find the are-length of a circle with the given radius r and central angle θ. Give the answer in the given unit of measure. r = 14 in; θ = 11 rad

Given cot²θ-3=0, -π≤0≤π a. Algebraically solve for θ. State the solution(s) as exact radian values.

A bicycle when with a radius of 13 inches turns with an angular velocity of 3 radians per second. Find the distance traveled by a point on the bicycle tire in 1 minute.

Use a power series to solve 2y"-y=0, y(0)=4, y'(0)=-9. Find the radius of convergence.

The graph of y=5^(x-13)+70 is the graph of y=5^x shifted how? State the direction of each shift followed by the number of units of that shift. (up/down)___ ___ units and (right/left)___ ___ units

The radioactive isotope Ra-226 has a half-life of about 1600 years. If 10 grams is present now, how much will be left 500 years from now? Round to the nearest thousandth of a gram. a) 8.912 grams b) 8.052 grams c) 7.839 grams d) 7.496 grams

Use matrices to solve the system. 5x+10y = 28.8 4x - 3y = 7.97

Solve the system by substitution. y = -2x - 2 3x + 2y = -1 The solution is

Convert the expression from degrees, minutes, seconds (DMS) notation to decimal notation. Round your answer to four decimal places. 67 11 17

Solve the equation. Approximate the solution(s) to the nearest hundredth. e²x-ex- 12 = 0

Find the solution set of the equation. log(5+x) -log(x - 3) = log 5 a) Ø b) {5} c) {-5} d) { 1³/12 }

Write the equation of the line with slope 1/9 and y-intercept 2.

Apply the change of base formula to rewrite log 4 (x - 3) in terms of natural logarithms.

Find r for the infinite geometric sequence. Determine whether the sum will converge. 1, 6, 36, 216, ...

Find the sum of the first 8 terms for the following arithmetic sequence. a4 = 12, a6 = 18

Rewrite sec40 in terms of the appropriate cofunction.

Find the arc-length of a circle with the given radius r and central angle θ. Give the answer in the given unit of measure. r = 52 cm; θ= 12 rad

Determine the amplitude, period, and phase shift of the following trigonometric equation. 3y = 1/2 sin (πx/4+ 2/3)

Find the coefficient a of the term in the expansion of the binomial. Binomial Terms (x-6y)10 ax8y² a. 1,619 b. 1,623 c. 1,620 d. 1,621 e. 1,618

Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 2π). Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution." 2√2cos(x) - 2 = 0

Bob wants to build an ice skating rink in his backyard, but his wife says he can only use the part beyond the wood-chipped path running through their yard. What would be the area of his rink if it is triangular-shaped with sides of length 18 feet, 23 feet, and 27 feet? Round to the nearest square foot.

Consider the following parametric equations: X = √t-1 and y = t - 4 Determine the domain and range of the equation obtained by eliminating the parameter. Please write your answer in interval notation.

A Freshman is planning for a trip to Europe when she graduates in 4 years. She estimates she will need $2000 to pay for the trip. If she has a savings account that earns 7.5% interest compounded monthly, how much does she need to deposit now to pay for her trip? Label your answer and round it to the nearest cent.

If a and n are integers, n > 0, then there exist integers q and r such that a = qn+r, where |r|<n/2.

The weights for 10 adults are 72, 78, 76, 86, 77, 77, 80, 77, 82, 80 kilograms. Determine the standard deviation. A. 4.28 B. 3.88 C. 3.78 D. 3.96

T-Mobile Park is home to the Seattle Mariners baseball team. For each game, the amount of money the team brings in as revenue is a function of the number of people in attendance. If the stadium seats 47929 people and the average ticket price is $30, what are the domain and range of this function?

Which of the following are true about a one-to-one function? Select all that apply. Its graph will pass both the vertical line test and the horizontal line test It will always have an inverse Its graph is symmetric around the origin Its graph will pass the horizontal line test but not the vertical line test It will always go through the point (1,1)

If f (a) = b, then which of these points is on the graph of f(x)? (a, b) (a, f(b)) (b, a) (f (a), f(b))

Suppose the function f(t) = 55000e0.061t gives the number of subscribers to a particular YouTube channel t years since 2015. Which of the following is true? The number of subscribers decreases as t increases. The number of subscribers increases as t increases. The number of subscribers remains constant as t changes.

Solve for the remaining angles and side of the triangle described below. Round to the nearest thousandth: B = 70, c = 6, a = 3

Which of the following situations would be best modeled by an exponential function? Select ALL that apply. The future value of an investment earning a constant interest rate. The decay of a radioactive element. The height of a baseball thrown in the air. The back and forth motion of a swing. The area of a circle as the radius increases.

Providence Park is home to the Portland Timbers soccer team. or each game, the amount of money the team brings in as revenue is a function of the number of people in attendance. If the stadium seats 25218 people and the average ticket price is $45, what are the domain and range of this function? Domain Range