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iren [92.7K]
3 years ago
11

Find the volume of a regular hexahedron if one of the diagonals of its faces is 8 root 2 inches.

Mathematics
1 answer:
Naily [24]3 years ago
8 0
The answer is 114sqrt{6} in³

A regular hexahedron is actually a cube. 

Diagonal of a cube D is a hypotenuse of a right triangle which other two legs are face diagonal (f) and length of a side (a):
D² = f² + a²

Face diagonal is a hypotenuse of a right triangle which sides are a and a:
f² = a² + a² =2a²

D² = f² + a²
f² = 2a²

D² = 2a² + a² = 3a²
D = √3a² = √3 * √a² = √3 * a = a√3

Volume of a cube with side a is: V = a³
D = a√3
⇒ a = D/√3

V = a³ = (D/√3)³

We have:
D = 8√2 in

V= (\frac{D}{ \sqrt{3} } )^{3} =( \frac{8 \sqrt{2} }{ \sqrt{3} } )^{3}=( \frac{8 \sqrt{2} * \sqrt{3} }{ \sqrt{3}* \sqrt{3}} )^{3} =( \frac{8 \sqrt{2*3} }{ \sqrt{3*3}} )^{3} =( \frac{8 \sqrt{6} }{ \sqrt{3^{2} }} )^{3} =( \frac{8 \sqrt{6} }{ 3} )^{3} = \\ \\ = \frac{ 8^{3} *( \sqrt{6} )^{3}}{3^{3}} = \frac{512* \sqrt{6 ^{2} }* \sqrt{6} }{27} = \frac{512*6* \sqrt{6} }{27} = 114sqrt{6}
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<h2>3</h2>

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<h3>Step 1: Identify two points on the line</h3>

1,2 & 2,5

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x1 = 2, y1 = 5     x2 = 1, y2 = 2

<h3>Step 3: Use the Slope Formula</h3>

change y/ change x

<u><em>IMPORTANT: it is change in y over change in x, not the other way around. It will be wrong if done the other way, though that would seem to be more logical, since x is the first variable in the pair.</em></u>

Y   5 -2 = 3        

X   2 - 1 = 1

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3 years ago
Help please!! Express the function graphed on the axes below as a piecewise function.
Aleksandr [31]

The piecewise function is:

f(x) = x + 1             if x < 2

f(x) = -7x + 42       if x > 5

<h3 /><h3>How to express the function graphed?</h3>

On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).

On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).

That line passes through (-1, 0) and (0, 1), then the slope is:

a = (1 - 0)/(0 -(-1)) = 1

And the y-intercept is y = 1, then the equation of the line is:

y = x + 1

The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)

The slope is:

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Then the line is something like:

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To find b, we use the point (6, 0)

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Then this line is:

y = -7x + 42

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If you want to learn more about piecewise functions:

brainly.com/question/3628123

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1 year ago
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Answer:

<h2>t = 10</h2>

Step-by-step explanation:

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