Answer:
If the area of a circle is 562 in², then the radius of the circle is about 13 inches long.
Step-by-step explanation:
![A = r^2\pi](https://tex.z-dn.net/?f=A%20%3D%20r%5E2%5Cpi)
![r = \sqrt{\frac{A}{\pi } }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%5Cfrac%7BA%7D%7B%5Cpi%20%7D%20%7D)
![r = \sqrt{\frac{562}{\pi } }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%5Cfrac%7B562%7D%7B%5Cpi%20%7D%20%7D)
![r = \sqrt{179}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B179%7D)
≈ ![13](https://tex.z-dn.net/?f=13)
We can see on this graph that the triangle has legs of x and 6 with a hypotenuse of 10 and we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem: a^2+b^2=c^2, where a and b are the legs of the triangle and c, is the hypotenuse
x^2+6^2=10^2 Plugin a=x, b=6, and c=10. Now let us solve for x
x^2+36=100 Square each individual term
x^2+=100+36 Subtract 36 from both sides
x^2=64 Combine like terms
sqrt(2)=sqrt(64) Take the square root of both sides
x = 8 Simplify the square root
So our answer is x = 8
The ladder touches the 8 feet mark on the wall.
The slope of a line is found as follows:
![Slope=\frac{rise}{run}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7Brise%7D%7Brun%7D)
In triangle ABC the slope of the hypotenuse is 1/3.
In triangle DFA the slope of the hypotenuse is 2/6 = 1/3.
The slopes of the two hypotenuses are equal, therefore the slope of k must be constant between points C and D.
The answer should be 10x²y²