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

konichiwa~! my name is zalgo and i am here to answer your anime-related question today. more than likely, kirishima would kill izuku, marry mino and kiss momo. all of this would be my opinion by the way. (and i am also a weeb lol)

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