The area of a circle is 1256 square inches what is the length of its radius

1 answer:

6 0

The formula of the area of a circle is : $A= \pi R^2$

You know that the area is 1256.

So : $1256= \pi R^2$

Divide both sides by $\pi$ :

$\frac{1256}{\pi}=R^2$

<span> take the square root of both sides in order to obtain r :

</span> $\sqrt{ \frac{1256}{ \pi }}=R$
$20=R$
<span>
In short, the answer would be 20 (i have rounded).

Hope this helps !

Photon
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The function f(x)=(x-5)^2 +2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the in

Anon25 [30]

We have been given a quadratic function $f(x)=(x-5)^{2} +2$ and we need to restrict the domain such that it becomes a one to one function.

We know that vertex of this quadratic function occurs at (5,2).

Further, we know that range of this function is $[2,\infty)$ .

If we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

Let us know find its inverse.

$y=(x-5)^{2}+2$

Upon interchanging x and y, we get:

$x=(y-5)^{2}+2$

Let us now solve this function for y.

$(y-5)^{2}=x-2\\
y-5=\pm \sqrt{x-2}\\
y=5\pm \sqrt{x-2}\\$

Hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .