rate of change of the area of the rebgion


by fifaking7
Tags: rate, rebgion
fifaking7
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#1
Nov10-12, 10:16 PM
P: 12
1. The problem statement, all variables and given/known data

A board 5 feet long slides down a wall. at the instant the bottom end is 4 feet from the wall, the other end is moving down the wall the rate of 2 feet per second.at that moment how fast is the area of the region between the board, the ground and the wall changing?

2. Relevant equations
a=1/2bh


3. The attempt at a solution
x^2 + 4^2= 5^2
x=3
da/dt= 1/2b(db/dt)(dh/dt)

I think i started it up wrong and I don't know where to go next..
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SammyS
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#2
Nov11-12, 01:03 AM
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Quote Quote by fifaking7 View Post
1. The problem statement, all variables and given/known data

A board 5 feet long slides down a wall. at the instant the bottom end is 4 feet from the wall, the other end is moving down the wall the rate of 2 feet per second.at that moment how fast is the area of the region between the board, the ground and the wall changing?

2. Relevant equations
a=1/2bh


3. The attempt at a solution
x^2 + 4^2= 5^2
x=3
da/dt= 1/2b(db/dt)(dh/dt)

I think i started it up wrong and I don't know where to go next..
What is the shape of the region below the board and above the ground at the moment under consideration?
fifaking7
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#3
Nov11-12, 01:42 AM
P: 12
just a normal triangle drawn on a line like a typical triangle leaning against a wall problem.

SammyS
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#4
Nov11-12, 01:49 AM
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rate of change of the area of the rebgion


Neither end of the board is touching the ground, so it's not a triangle.
aralbrec
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#5
Nov11-12, 01:49 AM
P: 296
Quote Quote by fifaking7 View Post
2. Relevant equations
a=1/2bh

da/dt= 1/2b(db/dt)(dh/dt)
Have another look at that derivative. It looks like the product rule hasn't been applied properly. Also one of those b/h is x. You'll have to stay consistent with your variable names.
fifaking7
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#6
Nov11-12, 01:26 PM
P: 12


that is how it looks
SammyS
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#7
Nov11-12, 01:44 PM
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Quote Quote by fifaking7 View Post


that is how it looks
You're right. I misread the problem.

When you said x=3, that should be h=3 .

In general, how are b and h related, considering that they're legs of a right triangle?
fifaking7
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#8
Nov12-12, 12:50 AM
P: 12
i said b= 4ft and h=3 ft
SammyS
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Nov12-12, 12:57 AM
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Quote Quote by fifaking7 View Post
i said b= 4ft and h=3 ft
That's what b & h are at the instant that h = 4 ft, but how are they related in general?

(Use the Pythagorean theorem.)
Ray Vickson
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#10
Nov12-12, 12:19 PM
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Quote Quote by fifaking7 View Post
i said b= 4ft and h=3 ft
The crucial point that you seem to be missing is that you need to figure out what is happening as the board slides down the wall, so h moves from more than 3 ft to less than 3 ft (and, at the same time, b moves from less than 4 ft to more than 4 ft). When that is happening, the area of the triangle is changing, and that is what you are supposed to be reckoning. So, you need to let b and h be variables, not fixed numbers.

RGV
SammyS
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#11
Nov12-12, 01:04 PM
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Quote Quote by SammyS View Post
That's what b & h are at the instant that h = 4 ft, but how are they related in general?

(Use the Pythagorean theorem.)
Of course, that's a typo !!!

It should have said:
That's what b & h are at the instant that b = 4 ft, but how are they related in general?


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