(a) Explain the purpose of changing variables when performing double or triple integration. (b) Post an example illustrating such a change of variables.

The pounds of bananas sold each week at all Metro Seattle Albertsons stores as a function of price, p , in dollars/pound(lb.) is given by q(p) = 100e7.5-1.5p1. Express the Revenue function in terms of p and then find both the first and second derivatives of the revenue function. Type each of these in your text box, using appropriate standard mathematical formatting notation (like that shown above) in Excel. 2. Use Excel over an interval of [0, 6] in increments of .25 to create values for all 3 of your functions from part 1. This is hard! You should be getting the beginning values shown on the next page. Keep at it until you do!! You must create these values by typing in and using the correct formulas. 3. Use Excel to determine exactly where there are any Maximum and/or Minimum values for Revenue. In your text box, explain fully and completely how you determine where to look, and how you know from the First Derivative Test that you have a maximum or a minimum value. 4. Write a…

We have a large tank filled with 50 liters of pure water. there is a salt solution of concentration 20 g/L flowing into the tank at a rate of 2 L/min. The well mixed solution is flowing out of the tank at a rate of 1 L/min. find the concentration  of salt in the tank as a function of time. no need to worry about the tank overflowing.

Following surgery, a patient has been receiving a pain relief medication intravenously. The concentration C (in milligrams per liter) of the medication in the patient's bloodstream t hours after this process started is given by C(t) a) The patient will not receive pain relief unless the concentration of the medication is 20 or more milligrams per liter. Use this function to determine the time interval for which the concentration of the medication, C, will be greater than or equal to 20 milligrams per liter. 60t + 12 t + 6 ,t≥ 0 The time interval for which the patient will receive pain relief is hours. (Express your answer in interval notation and round any decimals to the nearest tenth of an hour). b) If the intravenous medication continues to be given to the patient (that is, as time goes on and t approaches ∞), the concentration will approach milligrams per liter.

The growth rate of the population P of Horry county in South Carolina from 1970 through 2013 can be modeled bydP = 145.52t + 2002.3 dtwhere t is the time in years, with t = 0 corresponding to 1970. The county’s population was 289,650 in 2013. (Source: U.S. Census Bureau)(a) Find the model for Horry County’s population.(b) Use the model to predict the population in 2021. Does your answer seem reasonable? Explain your reasoning.

Fill in the blank. = F(s - a) whereas L eat dt = F(s - a) Need Help? Read It

A new fertilizer is being tested on a stalk of corn. The height of the corn is increasing in a linear fashion during the test period. The height of the corn t days after the fertilizer is first applied is given by H = 14 + 1.4t centimeters. Explain in practical terms the meaning of the initial value and growth rate. In practical terms this means "The corn's height when the fertilizer was applied was        and it grows by        ."

Differentiate the function. h(x) 4 5 - 4x3 + 1)8 4x + h'(x) = %3D

Explain the effect of α level on power?