Question

HELP PLEASE
A trough is 10 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 15 ft3/min, how fast is the water level rising when the water is 4 inches deep?

Answer 1

Looks like you need to find related rates for volume of the triangular prism and the altitude of the triangle.

Answer 2

You'll need a volume formula for the trough, a relation between volume and height, and then combine the derivatives.

Answer 3

Start with a volume formula in terms of the height, h.

Answer 4

we can do this

Answer 5

Satellite, please solve....I couldn't(

Answer 6

lets see first if we can find an equation for the volume given the height of the water

Answer 7

by similar triangles \(\frac{y}{x}=2.5\)
this gives \(y=2.5x\) and the area of the triangle \(5x^2\) i believe

Answer 8

oh no that is wrong, one half base times height, so \(2.5x^2\)

Answer 9

making the volume \(25x^2\) since we multiply the area of the triangle by the length of the trough

Answer 10

we get
\[V=25x^2\]
\[V'=50xx'\] we know \(V'= 15\) and we want \(x'\) when \(x=4\)

Answer 11

i get
\[15=200x'\]
\[x'=\frac{15}{200}\]

Answer 12

Oh Webassign says Incorrect((