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cluponka [151]
3 years ago
12

If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli's Law gives the v

olume V of water remaining in the tank after t minutes as V=5000(1−t40)20≤t≤40. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)
Mathematics
1 answer:
pochemuha3 years ago
4 0

Answer:

V'(t) = -250(1 - \frac{1}{40}t)

If we know the time, we can plug in the value for "t" in the above derivative and find how much water drained for the given point of t.

Step-by-step explanation:

Given:

V = 5000(1 - \frac{1}{40}t )^2  , where 0≤t≤40.

Here we have to find the derivative with respect to "t"

We have to use the chain rule to find the derivative.

V'(t) = 2(5000)(1 - \frac{1}{40} t)d/dt (1 - \frac{1}{40}t )

V'(t) = 2(5000)(1 - \frac{1}{40} t)(-\frac{1}{40} )

When we simplify the above, we get

V'(t) = -250(1 - \frac{1}{40}t)

If we know the time, we can plug in the value for "t" and find how much water drained for the given point of t.

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Answer: y = -4x + 1 or y = 1 - 4x

Step-by-step explanation:

First, we have to find the slope of the perpendicular. The slope of the line perpendicular to the other is the <u>reciprocal and opposite value</u> of the other line's slope.

This means that the slope perpendicular to y = 1/4x + 2 is -4, or -4/1.

Now we need to find the y-intercept, to do that we will use the equation y = mx + b. m = slope, b = y-intercept.

Plug in the values.

1 = -4(0) + b

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Now we can form the slope-intercept equation for the line perpendicular to y = 1/4x + 2 that passes through the point (0, 1).

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<span>The GCF of the numbers in the expression (55 + 44) is <u>11</u>. The numbers left inside the parentheses after factoring out the GCF are <u>5</u> and <u>4</u>. </span>



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