Answer:
Step-by-step explanation:
We have been given the formula of area of a circle and we are asked to write the formula of diameter in terms of the area of the circle.
![A=\pi r^2...(1)](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2...%281%29)
![d=2r...(2)](https://tex.z-dn.net/?f=d%3D2r...%282%29)
We will use substitution method to solve for d. From equation (2) we will get,
![\frac{d}{2}=\frac{2r}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B2%7D%3D%5Cfrac%7B2r%7D%7B2%7D)
![\frac{d}{2}=r](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B2%7D%3Dr)
Upon substituting this value in equation (1) we will get,
![A=\pi (\frac{d}{2})^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20%28%5Cfrac%7Bd%7D%7B2%7D%29%5E2)
![A=\pi *\frac{d^2}{4}](https://tex.z-dn.net/?f=A%3D%5Cpi%20%2A%5Cfrac%7Bd%5E2%7D%7B4%7D)
Let us multiply both sides of our equation 4.
![A*4=\pi *\frac{d^2}{4}*4](https://tex.z-dn.net/?f=A%2A4%3D%5Cpi%20%2A%5Cfrac%7Bd%5E2%7D%7B4%7D%2A4)
![4A=\pi *d^2](https://tex.z-dn.net/?f=4A%3D%5Cpi%20%2Ad%5E2)
Let us divide both sides of our equation by pi.
![\frac{4A}{\pi}=\frac{\pi *d^2}{\pi}](https://tex.z-dn.net/?f=%5Cfrac%7B4A%7D%7B%5Cpi%7D%3D%5Cfrac%7B%5Cpi%20%2Ad%5E2%7D%7B%5Cpi%7D)
![\frac{4A}{\pi}=d^2](https://tex.z-dn.net/?f=%5Cfrac%7B4A%7D%7B%5Cpi%7D%3Dd%5E2)
![d^2=\frac{4A}{\pi}](https://tex.z-dn.net/?f=d%5E2%3D%5Cfrac%7B4A%7D%7B%5Cpi%7D)
Let us take square root of both sides of our equation.
![d=\sqrt{\frac{4A}{\pi}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%5Cfrac%7B4A%7D%7B%5Cpi%7D%7D)
Therefore, the equation
represents the formula for diameter in terms of the area of the circle.
Answer:
-14 and 4
Step-by-step explanation:
To find the values subtract 9 from -5, as well as add 9 to -5
-5-9= -14
-5+9= 4
Answer:
4.5 or 4 1/2
Step-by-step explanation:
An easy way to do this problem is to divide 6 by 4, the denominator (1.5) then multiply it by the numerator, 3, which will now be 4.5.
So, for number 3, its 2. and for number 4 its also 2
Answer:
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