A trough is 9 feet long, and its cross section is in the shape of an isosceles right triangle with hypotenuse 2 feet, as shown above. Water begins flowing into the empty trough at the rate of 2 cubic feet per minute. At what rate is the height h feet of the water in the trough changing 2 minutes after the water begins to flow?

1/6

Step-by-step explanation:

Given:

=> The volume of the trough: V = * (b * h) (1)

=> the other two sides of the triangle is:

= tan(45 degrees) = h/(b/2)

<=> b = 2h   substitute in (1), we have:

V =  *(2h *h) = 9  

Take derivative of volume with respect to time to find equation for rate of filling the trough

dV/dt = 2 * 9 *h dh/dt = 18h dh/dt

<=> dh/dt = dV/dt /(18h)

As we know that, dV/dt = 2

So, dh/dt = 2 / 18h  = 1/9h

<=> V = t * rate = 2 * 2 = 4

But V = 9    

<=> 9     = 4

<=> h = 2/3  

The rate is the height h feet of the water in the trough changing 2 minutes after the water begins to flow:

dh/dt = 1/(9h) = 1/(9 * 2/3) = 1/6

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john wilson is depicted as an extremely intelligent man. the point of the excerpt is to make a sort of distinction between emotional and rational intelligence. he happens to have both attributes, but he clearly favors his intellectual gifts. at the same time, because of his religious background, he's a little bit conflicted with this and it makes him ashamed.

hope this !

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.