You are here:

# Calculus/Calculus

Question
Find dy/dx at (-2/3, 0) if    x3y2 - 2ey = 3x + y.
Enter the exact value (as a decimal).

Six-foot tall Barry is performing his last show at the world-famous copa-cabana lounge. The stage is 20 feet deep and has a spot light attached to the front edge (aimed back toward Barry) that casts a shadow on the back wall of the stage. Barry is singing and dancing his way toward the front edge of the stage at a rate of 5 feet per min. Find the rate at which the height of Barry's shadow is changing when he is 8 feet from the back wall.

It can be seen that 3x²y² + 2x³y - 2e^y = 3 + y'.
Subtract 3 from both sides, then put in both x=-2/3 and y=0.

Speed is 5'/m, distance is 8' from back wall, light is 20' from back wall, height is 6'.
The distance from the front of the stage is given by D(t) = 12 - 5t and his height is 6'.

It is known that the shadow height H(t) is given by H(t)/20 = 6/D(t)
since those are the height and base of two similar triangles.

Taking the derivative gives H'(t)/20 = -6D'(t)/D²(t).

We know at his point that D(t)=12 and D'(t)=-5 (since it is decreasing the distance).
Put thses in, mulitiply both sides by 20, and will give the speed that the shadow is growing at.  Note that we have a negative times a negatives, so the result is positive.
This means the shadow is increasing in height.

Calculus

Volunteer

#### 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 (reproduction, insusion of chemicals into bloodstream).

##### Experience

Experience in the area: I have tutored students in all areas of mathematics since 1980. 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 8,500 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 courses at college a year early.

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.