Sequences & Series Questions and Answers

θ is an acute angle and sin θ and cos θ are given. Use identities to find tan θ, csc θ, sec θ, and cot θ. Where necessary, rationalize denominators. sin θ = 24/25, cos θ = 7/25

An Enterprise company has an annual demand capacity of 40,000 units at a maintenance cost of $1. Currently, the company wants to reduce setup time by investing $111 to lower its current $1100 setup costs. It is hoped that this investment will result in a 2% reduction set up costs. Is this investment feasible if the expected rate of return on investment is 12%

To convert a degrees Celsius to y degrees Fahrenheit, we use the formula f(x) = 9/5x+32. Find the inverse function. ƒ-¹(x) =

Simplify. 5 log 5 (5x+2) 5 log 5 (5x + 2)

Express In ud as a sum of logarithms. In ud= (Simplify your answer.)

Express as a difference of logarithms. log b/p

A person purchased a house 10 years ago for $350,000. The house was financed by paying 20% down and signing a 15-year mortgage at 5.5% on the unpaid balance. Equal monthly payments were made to amortize the loan over a 15-year period. The owner (after the 120th payment) wants to sell the house. The net market value of the house is currently $700,000. How much equity to the nearest dollar does the person have in the house now?

In a triangle, the measure of the three angles of a triangle is180 °. In a triangle, the measures of the three angles are x, x+17, and x+16. What is the measure of each angle? The of the first angle, x is what?°

Determine the value of h in the translation. Describe the phase shift (use a phrase like "3 units to the left"). g(t) = f(t-3) Determine the value of h in the translation. h=

Assume that y = 2x and dx/ dt=6. Find dy/ dt.

a. 0.9= 0.90 A. The decimals 0.9 and 0.90 are equivalent because 0.90 can be represented by a decimal square with 9 of 10 columns shaded, and 0.9 is a decimal square with 90 of 100 parts shaded. Shading 90 of 100 parts is the same amount as shading 9 out of 10 columns. B.The decimals 0.9 and 0.90 are equivalent because 0.90 can be represented by a decimal square with 90 of 100 parts shaded, and 0.9 is a decimal square with 900 of 1,000 parts shaded. Shading 900 of 1,000 parts is the same amount as shading 90 of 100 parts. C. The decimals 0.9 and 0.90 are equivalent because 0.9 can be represented by a decimal square with 90 of 100 parts shaded, and 0.90 is a decimal square with 900 of 1,000 parts shaded. Shading 900 of 1,000 parts is the same amount as shading 90 of 100 parts. D. The decimals 0.9 and 0.90 are equivalent because 0.9 can be represented by a decimal square with 9 of 10 columns shaded, and 0.90 is a decimal square with 90 of 100 parts shaded. Shading 90 of 100 parts is the same amount as shading 9 out of 10 columns.

Find the critical point of the function. Then use the Second Derivative Test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) f(x, y) = xy +8/x +8/y critical point (x, y)= classification Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum value relative maximum value

Use the points (0, 4) and (-2, 3) to find the slope of the line and give the equation of this line.

John takes out a loan for $11800 at 7% interest compounded monthly and is making payments of $110 a month. Calculate his remaining balance after 18 months. John's balance due after 18 months will be $ 11232.39

In a particular year, a total of 59,130 students studied in two of the most popular host countries when traveling abroad. If 7294 more students studied in the most popular host country than in the second most popular host country, find how many students studied abroad in each country. There were ...students who studied abroad in the most popular host country.

Solve the system of equations. 3x + 9y = 51 4x+12y = 68 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is one solution. The solution of the system is (Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression B. The solution set of the system is {(x,y)|3x +9y=51}. C. The solution set is Ø.

Find an equation of the line. Slope 7; through (-3,2)

Find the equation of the line. Write the equation of the line in standard form. Vertical line; through (3,3).

Find the domain of the function f(x)=2-x¹/ x²-16 Let a sequence (x1)IEN be determined by the recurrence relation.

In ΔABC, C is a right angle. Find the remaining sides and angle Round your answers to the nearest tenth. a = 5, b = 6

An inflatable fishing boat leaves a dock at a bearing of N37°E. After running for 1.2 hr at 25 mph, how far north and east has it traveled? Round to the nearest mile. The boat travels approximately ... mi north and ...mi east.

3. Sketch a right triangle with 8 as the measure of one acute angle. Find the other five trigonometric ratios of 0. Leave in fraction form. Show your work. secθ =16/9

If we need $45,000 saved in 10 years, how much as a lump sum would we need to invest today at 9% compounded monthly?

Convert to a logarithmic equation. 64 1/3 = 4 The equation is. (Use integers or fractions for any numbers in the equation.)

6. Write an equation for each translation. a. y = sin x, π units to the left b. y = cos x, 3 units up

Find an angle A in degrees such that tan(A)=5.5027 where A terminates in QIII. Round your answer to the nearest degree.

Simplify the trigonometric expressions. Show your steps or give a reason for your answer. a. sec² θ - 1 b. sinθ cotθ

1. a = arctan (1/2) (use a calculator to find the answer for arctan(1/2), make sure the mode in your calculator is Radian), 2. b = arcsin (1/2), and 3. c = arccos(1/2). Then check out if a = b/c or not.

Determine where two asymptotes occur for the function. y = tan 4θ

Write a cosine function for each description. Assume that a > 0. a. amplitude 2, period π b. amplitude π, period 2

Graph the line with slope 3/4 passing through the point (3, 3).

Find the intercepts of the graph of 8x-3y = -24 Do not enter any spaces in the answers. The x-intercept is the point The y-intercept is the point

Write the equation for the linear function whose graph contains the points (1,-4) and (3,6). Write the answer in the form f(x) = mx+b.

Write the linear equation whose graph satisfies the given conditions. Perpendicular to the graph of 9y = 8 and passes through (-1, 12). Enter the answer in the form y = mx +b.

Which function's graph is the graph of f(x)=x² shifted down 20 units? a) g(x)=(x-20)² b) g(x) = (x+20)² c) g(x) = x² + 20 d) g(x)= x²-20

The graph of g(x) = (x - 10)³ is the graph of f(x) = x3 Shifted a) up 10 units. b) left 10 units. c) right 10 units. d) down 10 units.

The graph of g(x)=-x4 is the graph of f(x)=x4 reflected over which axis? a) the y-axis b) the x-axis

Which function's graph is the graph of f(x) = 1² shifted left 30 units and down 40 units? a) g(z) = (x+30)² + 40 b) g(z) = (x-30)² + 40 c g(z) = (x-30)² – 40 d g(x)= (x+30)² - 40

Solve the rational equation (1/x-3)+(5/x-2)=1/x^2-5x+6

Write the domain of the function in interval notation. h(x) = √x+8

Write the domain of the function in Interval notation. g(x)= x+2/ x-3

f(x) = 4x - 10 Find f(a-3). Simplify the result.

Which of the following represents the nth term of the arithmetic sequence below? Note that 65 is considered the 1st term. Select one: 65, 65.5, 66, 66.5, ... 65-0.5 (n − 1) 65+0.5 (n-1) 65+0.5n 65-0.5n

Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed cost is $100; 40 items cost $2,100 to produce. The linear cost function is C(x)=

Evaluate based on drawing a card from a standard deck of cards. Write your answer as a fraction in simplest form (a/b). P(club)

You must answer exactly 12 out of 15 questions on a test. How many different ways can you select the questions to answer?

explain my computation (why 3+3+3+1.5?). how does this compare to the traditional computation of 35% of 30= 0.35.30-10.5?

Write a sentence that illustrates the use of 7/8 in each of the following ways. a. As a division problem b. As part of a whole c. As a ratio

Suppose y varies inversely with x. and y = 5 when x = 3. What is the inverse variation equation that relates x and y ?

Use identities to find the indicated value. Where necessary, rationalize denominators. sin t = -27, cos t = -357 Find csc t.