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iragen [17]
3 years ago
9

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with

10-meter sides. The heights of the pyramids are the same. The volume of pyramid A is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is the volume of pyramid A.
Mathematics
2 answers:
drek231 [11]3 years ago
5 0

first is twice

second equal to

ollegr [7]3 years ago
4 0
Given:
Pyramid A: Base is rectangle with length of 10 meters and width of 20 meters.
Pyramid B: Base is square with 10 meter sides.
Heights are the same.

Volume of rectangular pyramid = (L * W * H) / 3
Volume of square pyramid = a² * h/3

Let us assume that the height is 10 meters.
V of rectangular pyramid = (10m * 20m * 10m)/3 = 2000/3 = 666.67 m³
V of square pyramid = (10m)² * 10/3 = 100m² * 3.33 = 333.33 m³

The volume of pyramid A is TWICE the volume of pyramid B.

If the height of pyramid B increases to twice the of pyramid A, (from 10m to 20m),  

V of square pyramid = (10m)² * (10*2)/3 = 100m² * 20m/3 = 100m² * 6.67m = 666.67 m³

The new volume of pyramid B is EQUAL to the volume of pyramid A.
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Answer:

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Step-by-step explanation:

Hi there!

We are given the line PQ and we want to find the line that is perpendicular to it

Perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1

So first, let's find the slope of the line PQ

The point P is given as (-8, 7) and the point Q is given as (-4, -5)

The formula for the slope calculated from two points is \frac{y_2-y_1}{x_2-x_1} where (x_{1} y_1) and (x_2, y_2) are points

We have the needed information for the slope, but let's label the values of the points to avoid any confusion

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Now substitute into the formula (m is the slope, and remember: the formula contains SUBTRACTION):

m=\frac{(-5-7)}{(-4--8)}

simplify

m=\frac{-5-7}{-4+8}

add

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divide

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So the slope of the line PQ is -3

As said above, perpendicular lines have slopes that have a product of -1

So to find the slope of the line perpendicular to PQ, use this formula:

-3m=-1

divide both sides by -3

m=1/3

The only line that has a slope of 1/3 is B (y=1/3x+4), so B is the answer.

Hope this helps!

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