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Katyanochek1 [597]
3 years ago
7

P and Q are similar hexagonal pyramids. The scale factor of P to Q is 6 : 1. If the volume of Q is 8 cubic yards, find the volum

e of P.
Mathematics
1 answer:
tatiyna3 years ago
8 0

Answer:

The volume of P is <u>1728 cubic yards.</u>

<u></u>

Step-by-step explanation:

For similar shapes, the ratio of volumes are defined as:

\frac{V_{1} }{V_{2}} = (\frac{h_{1} }{h_{2}}) ^{3}

where h1 and h2 are the heights of each pyramid respectively.

We know that the scale factor of P to Q is 6:1 i.e. the ratio of heights is also 6:1. And the volume of Q is given as 8 cubic yards. so, using the relation defined above we can write:

\frac{V_{P} }{V_{Q}} = (\frac{h_{P} }{h_{Q}}) ^{3}

\frac{V_{P} }{8} = (\frac{6}{1} )^{3}

Vp = 6³ * 8

     = 216 * 8

Vp = 1728 cubic yards

The volume of P is <u>1728 cubic yards.</u>

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Given,

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The quadratic sequence is :

3, 11, 25, 45, ...

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Now, According to the question;

The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.

The difference between the first and second terms can be calculated as follows:

11-3 = 8

The difference between the second and third terms can be calculated as follows:

25-11 = 14

The difference between the third and fourth terms can be calculated as follows:

45-25 = 20

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6(\frac{n(n+1)}{2} )

= 3n(n+1)

The sequence's nth term can be calculated as follows:

term = 3n(n+1) - 4n + 1

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USPshnik [31]
See the graph attached.

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In your case:
a = 0
b = 1
n = 4
x₀ = 0
x₁ = 1/4
x₂ = 1/2
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x₄ = 1

Therefore, you'll have:
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Hey there! I'm happy to help!

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