Question

A rectangle initially has width 4 meters and length 8 meters and is expanding so that the area increases at a rate of 9 square meters per hour. If the width increases by 20 centimeters per hour how quickly does the length increase initially?

Answer 1

Use the area of a rectangle equation:
\[A = lw\]
find the first derivative (rate of change of area) equation
\[A\prime = l(w)\prime + (l)\prime w\]
Solve for
\[(l)\prime \]
using the information

Answer 2

i got 50

Answer 3

did you convert the 20 cm per hour to 0.20 m per hour?

Answer 4

i believe i did, what did you come up with?

Answer 5

I got 1.85

Answer 6

1.85 m per hour

Answer 7

Did you use
\[A \prime = 9 m/hr, w = 4 m, l = 8m, w\prime = 0.20 m/hr\]

Answer 8

Yea, i meant the final answer.
I got 50

Answer 9

look at your algebra steps that can not be correct it is to large

Answer 10

ok so with 1.85, you did what after that?

Answer 11

That is what I get for the final answer after using the above numbers

Answer 12

@PhysicsGuru I understand why that should be the correct answer, but I don't understand why it doesn't work out when you try to take that answer and go back and figure out the area after x hours.

For instance, after 1 hour, at that rate, the length would be 9.85 and the width would be 4.2, which should be 32 + 9, but it's not quite. 9.85 x 4.2 = 41.37.

Answer 13

where are you getting 32 + 9?

Answer 14

The area at the beginning (4 meters x 8 meters = 32 square meters) plus the area after one hour, growing at a rate of 9 square meters per hour. 32 + 9 = area after one hour.

Answer 15

@PhysicsGuru can you just give me the answer and I can understand how it was derived from their