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Keith_Richards [23]
4 years ago
5

3.1 × 10^-4 in standard form

Mathematics
1 answer:
podryga [215]4 years ago
4 0

Answer:

Its 0.00031

Step-by-step explanation:

You just move your decimal the number of exponent. In your case -4 so you would move it to the left because it's a negative and move it 4 spaces.

Hope this helps!

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Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If the height increases at a consta
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Answer:

125\pi \frac{\text{ft}^3}{\text{min}}.

Step-by-step explanation:

Let x represent height of the cone.

We have been given that Sand pouring from a chute forms a conical pile whose height is always equal to the diameter.

We know that radius is half the diameter, so radius of cone would be \frac{x}{2}.

We will use volume of cone formula to solve our given problem.

V=\frac{1}{3}\pi r^2h

Upon substituting the value of height and radius in terms of x, we will get:

V=\frac{1}{3}\pi (\frac{x}{2})^2(x)

V=\frac{1}{3}\pi\frac{x^2}{4}(x)

V=\frac{1}{12}\pi x^3

Now, we will take the derivative of volume with respect to time as:

\frac{dV}{dt}=\frac{1}{12}\pi\cdot 3x^2\cdot \frac{dx}{dt}

\frac{dV}{dt}=\frac{1}{4}\pi\cdot x^2\cdot \frac{dx}{dt}

Upon substituting x=10 and \frac{dx}{dt}=5, we will get:

\frac{dV}{dt}=\frac{1}{4}\pi\cdot (10)^2\cdot 5

\frac{dV}{dt}=\frac{1}{4}\pi\cdot 100\cdot 5

\frac{dV}{dt}=\pi\cdot 25\cdot 5

\frac{dV}{dt}=125\pi

Therefore, the sand is pouring from the chute at a rate of 125\pi \frac{\text{ft}^3}{\text{min}}.

8 0
3 years ago
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