The formula for the nth term of a geometric sequence:
a₁ - the first term, r - the common ratio
![54, a_2, a_3, 128 \\ \\ a_1=54 \\ a_4=128 \\ \\ a_n=a_1 \times r^{n-1} \\ a_4=a_1 \times r^3 \\ 128=54 \times r^3 \\ \frac{128}{54}=r^3 \\ \frac{128 \div 2}{54 \div 2}=r^3 \\ \frac{64}{27}=r^3 \\ \sqrt[3]{\frac{64}{27}}=\sqrt[3]{r^3} \\ \frac{\sqrt[3]{64}}{\sqrt[3]{27}}=r \\ r=\frac{4}{3}](https://tex.z-dn.net/?f=54%2C%20a_2%2C%20a_3%2C%20128%20%5C%5C%20%5C%5C%0Aa_1%3D54%20%5C%5C%0Aa_4%3D128%20%5C%5C%20%5C%5C%0Aa_n%3Da_1%20%5Ctimes%20r%5E%7Bn-1%7D%20%5C%5C%0Aa_4%3Da_1%20%5Ctimes%20r%5E3%20%5C%5C%0A128%3D54%20%5Ctimes%20r%5E3%20%5C%5C%0A%5Cfrac%7B128%7D%7B54%7D%3Dr%5E3%20%5C%5C%20%5Cfrac%7B128%20%5Cdiv%202%7D%7B54%20%5Cdiv%202%7D%3Dr%5E3%20%5C%5C%0A%5Cfrac%7B64%7D%7B27%7D%3Dr%5E3%20%5C%5C%0A%5Csqrt%5B3%5D%7B%5Cfrac%7B64%7D%7B27%7D%7D%3D%5Csqrt%5B3%5D%7Br%5E3%7D%20%5C%5C%0A%5Cfrac%7B%5Csqrt%5B3%5D%7B64%7D%7D%7B%5Csqrt%5B3%5D%7B27%7D%7D%3Dr%20%5C%5C%0Ar%3D%5Cfrac%7B4%7D%7B3%7D)
a₁ - the first term, r - the common ratio
Need help learning 3rd grade perimeters n areas
1 answer:
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Answer:
(a) The volume of the pyramid 440.44 cube units
(b) No she doesn't
(c) The volume of the larger pyramid is 1,486.485 cube units
Step-by-step explanation:
The given parameters are;
The scale factor of the pyramids, S.F. = 2:3
The base area of the small pyramid, = 110.11 square units
The height of the small pyramid, h₁ = 12 units
(a) The volume of a pyramid, V = (1/3) × Area of base × The height of the pyramid
Therefore;
The volume of the small pyramid, V₁ = (1/3) × 110.11 square units × 12 units
V₁ = 440.44 cube units
The volume of the small pyramid, V₁ = 440.44 cube units
(b) No she does not have to go through all the hard work again to find the volume of the larger pyramid
She only has to make use of the scale factor relationships of the two pyramid to calculate the volume of the larger pyramid
The volume scale factor = (The linear scale factor)³
(c) The linear scale factor of the pyramids = 2:3 = 2/3
Therefore;
The volume scale factor of the pyramids = (2/3)³ = 8/27
To find the volume of the larger pyramid, V₂, from the volume of the smaller pyramid, V₁, we multiply the volume of the smaller pyramid, V₁, by 27/8 as follows;
V₂ = V₁ × (27/8)
Therefore;
The volume of the larger pyramid, V₂ = 440.44 cube units × (27/8) = 1,486.485 cube units
The volume of the larger pyramid, V₂ = 1,486.485 cube units.
Unfortunately, there are no two such numbers.
If your original question was:
and you were trying to factor it, I would suggest the quadratic formula.
There are two solutions to
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So using that, here is how it would get factored:
For your equation,
Plug in those values into the formula:
Simplifying it:
And so the solutions are:
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If your original question was:
There are two solutions to
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So using that, here is how it would get factored:
For your equation,
Plug in those values into the formula:
Simplifying it:
And so the solutions are:
and