If you can rewrite the formula as (x-a)² + (y-b)² = r², the center is at (a,b) and the radius is r.
If you work out this equation, and map it to the original, you will find that the +4x term hints that a = 2 (double product) and -12y hints that b=-6, and r=6.
So, the formula can be written as (x+2)² + (y-6)² = 6² and the center is at (-2,6) and the radius is 6.
B
To solve for the inverse, just swap the x and y and solve for the new y.
![y=\sqrt{x} -8](https://tex.z-dn.net/?f=y%3D%5Csqrt%7Bx%7D%20-8)
![x=\sqrt{y}-8](https://tex.z-dn.net/?f=x%3D%5Csqrt%7By%7D-8)
![x+8=\sqrt{y}](https://tex.z-dn.net/?f=x%2B8%3D%5Csqrt%7By%7D)
![(x+8)^2=y](https://tex.z-dn.net/?f=%28x%2B8%29%5E2%3Dy)
Then inspect both functions for the domain.
In the original function, x has to be greater than or equal to 0 or else you would have a negative square root which is impossible.
The inverse function has no limitations as any x could make that true.
The main things that will limit domain is square root of negative or divide by zero.
Therefore, x>=0 is the only domain restriction.
The ideal radius Alan must control is
cm.
<h3>Define perimeter of circle.</h3>
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The area of a circle determines the space it takes up. A circle's diameter is equal to the length of a straight line traced through its center. Usually, it is stated in terms of units like cm or m.
Given data -
Perimeter of circular plate = 10
cm
We know that perimeter of a circle is 2
r
Therefore 10
= 2
r
r = 5 cm
The given error Alan can make is +-1 cm.
Minimum radius is given by
2
r = 10
- 1
r = ![\frac{10\pi - 1 }{2\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B10%5Cpi%20-%201%20%7D%7B2%5Cpi%20%7D)
r = 5 - ![\frac{1}{2\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%5Cpi%20%7D)
Maximum radius is given by
2
r = 10
+ 1
r = ![\frac{10\pi + 1 }{2\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B10%5Cpi%20%2B%201%20%7D%7B2%5Cpi%20%7D)
r = 5 + ![\frac{1}{2\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%5Cpi%20%7D)
The ideal radius Alan must control is
cm.
To know more about perimeter of circle, visit:
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Answer: y=-0.5x+4.5
Step-by-step explanation: y=mx+b, m is the slope = -1/2 or -0.5, and b is the y-int, which is 4.5
Sqrt (y^4 * y)
Sqrt y*4 = y^2
y^2 sqrt y