Answer:
1/6
Step-by-step explanation:
Given:
- Length of the trough: 9 ft
=> The volume of the trough: V =
* (b * h) (1)
- An isosceles right triangle with hypotenuse 2 feet
=> 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
Answer:
If you multiply 256 by 10 powered by k, then the number of zeros in the product is k
Step-by-step explanation:
Let x be any integer, if you multiply x by 10 you will have to add one zero at the right of x. If you multiply by 10 again, you will have to add a second zero at the right, thus if you multiply by 100, you will have to add 2 zeros. If you multiply by 1000 = 10*10*10 = 10³ you will have to add 3 zeros and so on.
Therefore, if you multiply 256 by 10^k, then you will have to add k zeros to 256, and as a consequence, the amount of zeros in the product is equal to the power of 10 we are multiplying.
There are 4 cups in one quart, so if you do 2 1/2 times 4 you will get 10. That means the pitcher holds 10 cups.
An integer is a whole number that can be positive, negative, or zero.
