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2 years ago

Determine the height of a square pyramid with a volume of 225 cubic inches and a base edge of 5 inches.

Mathematics

1 answer:

ss7ja [257]2 years ago

5 0

Answer:

h = 27 inches

Step-by-step explanation:

Given that,

The volume of a square pyramid, V = 225 inches³

The base edge of a square pyramid, b = 5 inches

We need to find the height of a square pyramid. The formula for the volume of a square pyramid is given by :

$V=\dfrac{1}{3}B\times h$

B is area of base, B = b²

So,

$h=\dfrac{3V}{b^2}\\\\h=\dfrac{3\times 225}{5^2}\\\\h=27\ \text{inches}$

So, the height of the square pyramid is 27 inches.

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Can someone help me

kolbaska11 [484]

m < 1 = 130°

m < 1 = 130°m < 2 = 50°

We know this is a linear pair, therefore the two angles must add up to 180°

$(m < 1 )+ (m < 2 )= 180$

$5x + x + 24 = 180$

Combine like terms

$6x + 24 = 180$

Isolate the variable

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Plug in 26 for x in both of the individual angle equations.

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A good way to check if we did this correctly, is to add up the two angles. Because 180 + 50 = 180, we did this correctly.

I hope this helped. Let me know if you have any questions!

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3 years ago

What happens to the distance between each billiard ball during this rigid transformation?

Delicious77 [7]

The question is incomplete. Here is the complete question.

To set up a game of billiards, the first player moves the balls contained within a triangular rack as shown. What happens to the distance between each billiard during this rigid transformation?

A. The distance remains constant throughout the transformation.

B. The distance decreases at the start and increases after all motion stops.

C. The distance stays the same at the start but decreasesexactly when motion ends.

D. The distance increases at the start and then decreases as the rack gets further from the player.

Answer: A. The distance remains constant throughout the transformation.

Step-by-step explanation: In a rigid motion, all moving points in the plane are moving in way such tha:

1) relative distance between them stays the same and

2) relative position of the points stays the same

There are four types of rigid motions: translation, rotation, reflexion and glide reflection.

Translation: every point or object is moved by the same amount and in the same direction;

Rotation: the object rotates by the same amount around a fixed point;

Reflexion: the object exchange points from one side of a line with points on the other side of the line at the same distance from the line;

Glide Reflection: is a mirror reflection followed by a translation parallel to the mirror.

In the game of billiards, because all the balls are inside the triangular rack, the distance, and also the position, between them stays the same, limited by the rack. Since they are moving by the same amount in the same direction, the rigid transformation is a translation.

Therefore, the distance of the balls in the triangular rack remains constant throughout the transformation.

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