Sketch and find the area of the region bounded by the curves ?=?+? and ?=?²−?.

Suppose the average yearly salary of an individual whose final degree is a master's is $3333 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $117 thousand. Find the average yearly salary of an individual with each of these final degrees.

The volume of a right circular cylinder with base radius ? and height ℎ is given by: ? = ??^2ℎ. If the base radius is decreasing at a rate of 3 inches per minute and the height is increasing at a rate of 2 inches per minute, at what rate is the volume of the cylinder changing when the radius is 8 inches and the height is 3 inches. Will the volume be increasing or decreasing at this instant? Be sure to answer both questions and be sure to include units in your answer.

A trough is filled with a liquid of density 820 kg/m³. The ends of the trough are equilateral triangles with sides 6 m long and vertex at the bottom. Find the hydrostatic force on one end of the trough. (Use 9.8 m/s² for the acceleration due to gravity.)

The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y = 0.5 x ^2 and below the line y = 280 . (Here, distances are measured in meters.) The water level is 34 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000 kg/ m^ 3 , and the acceleration of gravity is 9.8 m/ sec ^2 .)

Answer in Newtons and make sure that it is not in scientific notation. Check answer as last 5 have been wrong answers. Need detailed steps also

COURSE TITLE:Business Research Methods and Statistical Analysis

TOPIC:Literature Review

Q1/Consider the topic of study is STUDY ON IMPACT OF PERFORMANCE APPRAISAL FEEDBACK ON JOB SATISFACTION AND ITS IMPACT ON ORGANISATION COMMITMENT and prepare the chapter two below points. It must fulfill all the headings of the chapter two

Chapter 2 – Review of Related Literature and Studies

2.1 Related Literature

2.2 Related studies

2.3 Syntheses

Note: Page range between 8 to 15 pages

Find the Maclaurin series of f(x) = [sin(x²)]/x and find its radius of convergence.

1. Find the balance after 5 years in a savings account that pays 2.5% APR compounded monthly if deposits are made to the account each month in the amount of $100.

2. A friend has an IRA with an APR of 6.25%. She stared the IRA at age 25 and deposits $50 per month.
          a) How much will her IRA contain when she retires at age 65?
          b) How much money did she contribute to the account?
          c) Use the answers from parts a) and b) to determine the amount of interest earned.

3. What if your friend from question #2 doubled her deposit and saved $100 per month? Do you think her money would double? Let's find out! Redo question #4, all the parts, with a monthly deposit of $100 per month. Were you surprised by the results?

4. At age 35 you start saving for retirement. Your investment plan pays 6% APR compounded monthly and you want to have $2,000,000 when you retire at age 65.
        a) How much do you need to save each month?
        b) Suppose you had started saving when you were 30 years old. How much would you need to save each month?
        c) Suppose you had started saving when you were 25 years old. How much would you need to save each month?
        d) Were you surprised by the answers in parts a - c? Discuss the effect of time on the growth of money.

Use calculus to find three positive numbers that sum to 150 with the greatest possible product.

Solve the following initial value problem using Laplace transforms:
y000 + y0 = et, y(0) = y0(0) = y00(0) = 0.

Solve the initial value problem once using power series method and once using the characteristic method. Please show step for both 3) 3y”−y=0, y(0)=0,y’(0)=1

Note that 3y” refers to it being second order differential and y’ first

Market Research:

You have an apple orchard. You let people pick their own apples. When you let people pick a small bag for $6, there were 6,316 small bags sold. You do some market research and find that a $0.25 increase in price means 235 fewer small bags of apples sold. Recall that revenue is quantity sold X Price per quantity. If we let x be the number of $0.25 increases or decreases from $6 and R be revenue, then answer the following questions:

A) What equation represents what you expect the revenue to be based on your research?

B) Based on your answer in A, if you charge $5.75 (x= -1) how much do you expect the revenue to be?

C) At what price or prices will you have $30,000 in sales, If your expectations listed above are true?

I would appreciate any and all help. If you give the answers, could you please show work and explain how you got them? I did my best in trying to re-write the questions (my professor doesnt have great grammar.)

Let (R 3 , ×) be the set of 3d vectors equipped with the operation of vector crossproduct. Which of the following properties does this operation satisfy (give proofs in all cases)?

(a) has identity element(s)? (If so, determine all identity elements.)

(b) has idempotent element(s)? (If so, determine all idempotent elements.)

(c) commutative?

(d) associative?

2. Find the point on the line 6x+y=9 that is closest to the point (-3,1).

a. Find the objective function.

b. Find the constraint.

c. Find the minimum (You need to specify your method)