Answer:
<h2>The radius is 4 units long.</h2>
Step-by-step explanation:
The given equation is

This equation belongs to a circle, which center is at (0.5, 3.5) and its radius is 4.
You can deduct its elements, becase this equation of the circle is explicit, which means the constant term represents the square power of the radius. Solving that, we have

Therefore, the radius is 4 units long.
This is the concept of algebra, suppose that the number of cats is x;
number of cats will be x-20
number of rabbits will be 3/2x
thus the total number of animals will be:
x+(x-20)+3/2x=350
7/2x=350+20
7/2x=370
x=370*2/7
x=105.7=106
therefore we conclude that there we 106 cats in the shelter
I think the answer is c= 0.248
Answer:

General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Product Rule]: ![\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29g%28x%29%5D%3Df%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- [Function] Derivative Rule [Product Rule]:
![\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B9x%5E%7B10%7D%5D%20%5Ctan%5E%7B-1%7D%28x%29%20%2B%209x%5E%7B10%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctan%5E%7B-1%7D%28x%29%5D)
- Rewrite [Derivative Property - Multiplied Constant]:
![\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%209%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E%7B10%7D%5D%20%5Ctan%5E%7B-1%7D%28x%29%20%2B%209x%5E%7B10%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctan%5E%7B-1%7D%28x%29%5D)
- Basic Power Rule:
![\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%2090x%5E9%20%5Ctan%5E%7B-1%7D%28x%29%20%2B%209x%5E%7B10%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctan%5E%7B-1%7D%28x%29%5D)
- Arctrig Derivative:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation