# Could someone please check over my homework?

#### ugeous

Hey guys!

There are two topics I am not 100% sure with, so I am asking you to please check over my homework. I did not do the best on the quizzes, so it is very important for me to get a perfect mark on these two assignments. Thank you very much for helping me out!

Derivative Applications

1. A trough in the cross sectional shape of an inverted equilateral triangle is being filled at a rate of 355 cm3/min. The trough is 2 m long and has a side length of the triangle of 25 cm. How fast is the water level rising when the water is 12 cm deep? (5 marks)

2. A hotel owner knows that all 400 rooms can be rented for $85 per night. She also knows that for every$5 increase in price, 12 fewer rooms will be rented. How much should she charge per room to maximize her revenue? (5 marks)

3. A 1.85 m tall man is walking toward a 12 m tall street light at night at a rate of 2.2 m/s. How fast is the length of his shadow changing when he is 12 m from the street light? (5 marks)

4. A rectangular prism has its length increasing by 12 cm/min, its width increasing by 4 cm/min and its height increasing by 2 cm/min. How fast is it's volume changing when the dimensions are 200 cm in length, 50 cm in width and 30 cm in height? (5 marks)

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Derivative of Exponential and Log Functions

1) Find the derivative of the following functions.
a) y = (2^x)/(e^x)
b) f(x) = 2x ln(x^2 + 5)
c) g(x) = (lnx)/(e^(x^2+2))

2) If s(t) = ln(3t^2 + t) find the slope of the function at t = 2.

3) Find dy/dx for the function xy^2 + x lnx = 4y for x>0

4) Graph the function y = e^(-x^2)

5) Use logarithmic differentiation to find dy/dx for ((x + 1)^2(x + 3))/(square root(x^2 + 1)) at x=0

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#### Mark44

Mentor
Speaking for myself, it's a lot of work to look at each of your problems and verify that you have done them correctly. Judging by the lack of activity, I think there are other people in the forum who feel the same way.

You will have a better chance of getting a response if you ask about one problem.

#### berkeman

Mentor
Speaking for myself, it's a lot of work to look at each of your problems and verify that you have done them correctly. Judging by the lack of activity, I think there are other people in the forum who feel the same way.

You will have a better chance of getting a response if you ask about one problem.
Agreed. The Homework Help forums and its volunteers are not really suited to such detailed homework checks.

Instead, consider checking your own work, by doing it a different way and seeing if you get the right answer. Like on #2, you could use a quick Excel spreadsheet calculation to check your work. And if you are calculating a derivitave, do an integration to check your work to within a constant of integration.

After you try to check your work as best you can, if you end up with one problem that you are having trouble checking, post all of your work and we'll try our best to help out.

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