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3 years ago

Find three consecutive odd integers such that the first is 33 less than twice the second

Mathematics

1 answer:

34kurt3 years ago

6 0

n, n + 2, n + 4 - three consecutive odd integers

the first is 33 less than twice the second

n - 33 = 2(n + 2) <em>use distributive property</em>

n - 33 = (2)(n) + (2)(2)

n - 33 = 2n + 4 <em>add 33 to both sides</em>

n = 2n + 37 <em>subtract 2n from both sides</em>

-n = 37 <em>change the signs</em>

n = 37

n + 2 = 37 + 2 = 39

n + 4 = 37 + 4 = 41

<h3>Answer: 37, 39, 41</h3>

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Answer:

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Step-by-step explanation:

A gallon equals 0.134 cubic feet. First, we determine the amount of water ( $Q$ ), measured in cubic feet, needed to put out the fire under the assumption that water is consumed at constant rate:

$Q = \dot Q \cdot \Delta t$ (1)

Where:

$\dot Q$ - Volume rate, measured in feet per minute.

$\Delta t$ - Time, measured in minutes.

If we know that $\dot Q = 2000\,\frac{gal}{min}$ and $\Delta t = 120\,min$ , then the amount of water is:

$Q = \left(2000\,\frac{gal}{min} \right)\cdot (120\,min) \cdot \left(0.134\,\frac{ft^{3}}{gal} \right)$

$Q = 32160\,ft^{3}$

And the diameter of the cylindrical tank based on the capacity found above is determined by volume formula for a cylinder:

$Q = \frac{\pi}{4}\cdot D^{2}\cdot h$ (2)

Where:

$D$ - Diameter, measured in feet.

$h$ - Height, measured in feet.

If we know that $Q = 32160\,ft^{3}$ and $h = 12\,ft$ , then the minimum diameter is:

$D^{2} = \frac{4\cdot Q}{\pi\cdot h}$

$D = 2\cdot \sqrt{\frac{Q}{\pi\cdot h} }$

$D = 2\cdot \sqrt{\frac{32160\,ft^{3}}{\pi\cdot (12\,ft)} }$

$D \approx 58.415\,ft$

The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.

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2 years ago

An angle is 6 more than five times its supplement. Find the measure of the largest angle.

Julli [10]

Supplementary angles add up to 180°

Angle y is the large angle: y= 5x+6

180= x+y
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180= y+29
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Dahasolnce [82]

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Step-by-step explanation:

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