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3 years ago

X^2 + 16 Factor the polynomial completely

Mathematics

1 answer:

Lelu [443]3 years ago

5 0

Step-by-step explanation:

${x}^{2} + {16} \\ {x}^{2} + {4}^{2} \\(x + 4 {)}^{2} \\ = {x}^{2} + 8x + 16$

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Step-by-step explanation:

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2 years ago

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Jim’s backyard is rectangular with dimensions of 80 feet by 120 feet. He is planning to designate part of the yard to plant a ve

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1 year ago

Answer Choice

melisa1 [442]

Answer:

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Step-by-step explanation:

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2 years ago

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3 years ago

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

Cerrena [4.2K]

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

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3 years ago