Step-by-step explanation:
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The answer for this will be letter d. C = 22π and A = 121π. This is computed using the formula of C= Dπ which is C = (22)π. On the other hand, the area of this circle is computed by using the formula A = <span>πr^2. This is computed as follows:
A = </span><span>πr^2
A = </span><span>π (22/2)^2
A = </span><span>π (11)^2
</span>A = 121<span>π</span><span>
</span>
ANSWER
![{a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B3%7D%20%20%2B%20%7Bb%7D%5E%7B3%7D%20%3D%20%28a%20%2B%20b%29%28%20%7Ba%7D%5E%7B2%20%7D%20%20-%20ab%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%29)
EXPLANATION
To find the expression that is equivalent to
![{a}^{3} + {b}^{3}](https://tex.z-dn.net/?f=%7Ba%7D%5E%7B3%7D%20%20%2B%20%7Bb%7D%5E%7B3%7D)
we must first expand
![{(a + b)}^{3}](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20b%29%7D%5E%7B3%7D%20)
Then we rearrange to find the required expression.
So let's get started.
![{(a + b)}^{3} = (a + b) {(a + b)}^{2}](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20b%29%7D%5E%7B3%7D%20%20%3D%20%28a%20%2B%20b%29%20%7B%28a%20%2B%20b%29%7D%5E%7B2%7D%20)
We expand the parenthesis on the right hand side to get,
![{(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20b%29%7D%5E%7B3%7D%20%20%3D%20%28a%20%2B%20b%29%20%28%20%7Ba%7D%5E%7B2%7D%20%2B%202ab%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%29)
We expand again to obtain,
![{(a + b)}^{3} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3}](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20b%29%7D%5E%7B3%7D%20%20%3D%20%20%7Ba%7D%5E%7B3%7D%20%20%2B%203%20%7Ba%7D%5E%7B2%7Db%20%2B%203a%20%7Bb%7D%5E%7B2%7D%20%20%20%2B%20%20%7Bb%7D%5E%7B3%7D%20)
Let us group the cubed terms on the right hand side to get,
![{(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2}](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20b%29%7D%5E%7B3%7D%20%20%3D%20%20%7Ba%7D%5E%7B3%7D%20%20%20%2B%20%20%7Bb%7D%5E%7B3%7D%20%20%2B%203%20%7Ba%7D%5E%7B2%7Db%20%2B%203a%20%7Bb%7D%5E%7B2%7D%20)
![{(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20b%29%7D%5E%7B3%7D%20%20%3D%20%20%7Ba%7D%5E%7B3%7D%20%20%20%2B%20%20%7Bb%7D%5E%7B3%7D%20%20%2B%203ab%20%28a%2B%20b%29)
We make the cubed terms the subject,
![{(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3}](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20b%29%7D%5E%7B3%7D%20%20-%203ab%20%28a%2B%20b%29%20%3D%20%20%7Ba%7D%5E%7B3%7D%20%20%20%2B%20%20%7Bb%7D%5E%7B3%7D%20%20)
We factor to get,
![(a + b)({(a + b)}^{2} - 3ab ) = {a}^{3} + {b}^{3}](https://tex.z-dn.net/?f=%20%28a%20%2B%20b%29%28%7B%28a%20%2B%20b%29%7D%5E%7B2%7D%20%20-%203ab%20%29%20%3D%20%20%7Ba%7D%5E%7B3%7D%20%20%20%2B%20%20%7Bb%7D%5E%7B3%7D%20%20)
We expand the bracket on the left hand side to get,
![(a + b)( {a}^{2} + 2ab + {b}^{2} - 3ab ) = {a}^{3} + {b}^{3}](https://tex.z-dn.net/?f=%20%28a%20%2B%20b%29%28%20%7Ba%7D%5E%7B2%7D%20%20%2B%202ab%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%20-%203ab%20%29%20%3D%20%20%7Ba%7D%5E%7B3%7D%20%20%20%2B%20%20%7Bb%7D%5E%7B3%7D%20%20)
We finally simplify to get,
The critical points of the function graphed are given as follows:
<h3>What are the critical points of a function?</h3>
The critical points of a function are the values of x for which:
![f^{\prime}(x) = 0](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%200)
In a graph, they are turning points, and are classified as follows:
- Local maximum, if the functions changes from increasing to decreasing.
- Local minimum, if the functions changes from decreasing to increasing.
Looking at the graph, the turning points are approximately:
More can be learned about critical points at brainly.com/question/2256078
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Answer:
60
Step-by-step explanation:
Plug it into the calculator