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About Scotto
Expertise
Any kind of mathematics (calculus, analysis, game theory, linear approximation, finite differences, linear regression, linear programming, numerical analysis, probability, statistics, etc.). I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience
Experience in the area: I have tutored students in all areas of mathematics for over 20 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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Maybe not a publication, but I have respond to well oveer 3000 questions on the PC. That's around 2,000 in basic math and 1,000 in advanced math.

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I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

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I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

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My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you.

 
   

You are here:  Experts > Teens > Homework/Study Tips > Calculus > rate of change in rectangle

Calculus - rate of change in rectangle


Expert: Scotto - 7/10/2008

Question
I'm having difficulty setting these equations up.  Any help would be greatly appreciated!

Robert

The length, L, of a rectangle is decreasing at the rate of 2cm/second while the width, W, is increasing at the rate of 2cm/second.  When L = 12cm and W = 5cm, find the rates of change of the area, the perimeter, and the lengths of the diagnol of the rectangle.

Answer
dL/dt = -2, dW/dt = 2, L=12, W=5

Area is A=WL, perimeter is P=2W+2L, lengths of the diagonal of the rectangle is C=Sqrt(W²+L²).

Note that A, P, and d are all functions of W and L.  Using the chain rule, find dA/dt, dP/dt, and dC/dt.

dA/dt = (dW/dt)L +W(dL/dt), dP/dt=2(dW/dt) + 2(dL/dt).
dC/dt = (W+L)/Sqrt(W²+L²).

Put in the value given at the top into the equations just given to get the answer.

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