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2 years ago

Find the surface area of the composite figure.

Mathematics

1 answer:

9966 [12]2 years ago

4 0

The surface area of the composite figure shown in the image is 952 ft²

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Surface area of composite is the sum of the individual areas of the surface.

Hence:

Surface area of composite = 2(14 * 9) + 2(0.5 * 10 * 8) + 2(10 * 10) + 2(10 * 14) + (10 * 14) = 952 ft²

The surface area of the composite figure shown in the image is 952 ft²

Find out more on equation at: brainly.com/question/2972832

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Solve the following recurrence relation: <br> <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

$\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}$

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2 years ago

Is -7 + 28 positive or negative?

stepan [7]

Answer:

Positive

Step-by-step explanation:

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21 is positive

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3 years ago

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3 years ago

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sergij07 [2.7K]

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Find the surface area of the composite figure.​

Find the surface area of the composite figure.