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Calculus/related rates
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Question
The base of a pyramid-shaped tank is a square with sides of 8 meters long and the vertex of the pyramid is 11 meters above the base. The tank if filled to a depth of 4 meters and water if flowing into the tank at the rate of 2 cubic meters per minute. Find the rate of change of the depth of the water in the tank.
Let x be how high we are from the ground. The width at the ground is 8 and the width at height 11 is 0. That's a linear equation that can be found. Using that line, the depth at 4 meters can be found to be 4/11 of 8. Square this value and that will be the cross sectional area at this depth. Take 2 divided by this value and that will be the rate of change of depth at that point.
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Answers by Expert:
Scotto
Expertise
Any kind of calculus question you want. 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 25 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.
Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC.
Well over 2,000 of them have been in calculus.
Education/Credentials
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.
Awards and Honors
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).
Past/Present Clients
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 from all over the world.
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