More help with Calculus

Discus: SAT/ACT Tests and Test Preparation: October 2003 Archive: More help with Calculus
 By Screwed4life (Screwed4life) on Tuesday, October 14, 2003 - 08:31 pm: Edit

Hey I posted some questions on implicit differentian above but i also need help on relative rates..I understand some..but not all of them. I need help with 2 problems.

A 5-meter-long ladder is leaning against the side of a house. The foot of the ladder is pulled away rom the house at a rate of 0.4 m/sec. Determine how fast the top of the ladder is descending when the foot of the ladder is 3 meters from the house.
a. 1.2 m/sec
b. -1.2 m/sec
c. 0.3 m/sec
d. -0.3 m/sec
e. None of these

A spherical balloon is inflated at the rate of 16 cubic feet per minute. How fast is the radius of the baloon changing at the instant the radius is 2 feet.
a 4"Pie"
b.32/3"pie"
c. 1/pie
d. 2"pie"
e none of these

And can you all show me your work. The first problem is i think a 3-4-5 triangle..but i don't know what else to do with it

 By Justice (Justice) on Tuesday, October 14, 2003 - 10:19 pm: Edit

1)
Imagine a triangle that has hypotenuse d, and legs x and y on their respective axis in a coordinate plane.

They ask you for dy/dt when x = 3. They give you dx/dt which is 0.4. They tell you d, which is obviously a constant (the ladder is not going to start growing). Thus, at x = 3, y = 4 by route of 25-9 = y^2.
Choose D.

Relationship:
d^2 = x^2 + y^2
Differentiation:
0 = (2x)(dx/dt) + (2y)(dy/dt)
0 = (6)(.4) + (8)dy/dt
dy/dt = -0.3