we have M is durectly porpotional to r^2
so M=(k)r^2
and when r=2, m=14
so 14=(k)(2)^2
k=14/4 =7/2
so when r=12
m= (7/2)(12)^2 =(7/2)(144) = 504
Answer:

Domain: All Real Numbers
General Formulas and Concepts:
<u>Algebra I</u>
- Domain is the set of x-values that can be inputted into function f(x)
<u>Calculus</u>
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Derivative: ![\frac{d}{dx} [ln(u)] = \frac{u'}{u}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bln%28u%29%5D%20%3D%20%5Cfrac%7Bu%27%7D%7Bu%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = ln(2x² + 1)
<u>Step 2: Differentiate</u>
- Derivative ln(u) [Chain Rule/Basic Power]:

- Simplify:

- Multiply:

<u>Step 3: Domain</u>
We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.
Therefore, our domain would be all real numbers.
We can also graph the differential function to analyze the domain.
Answer:
90m+145
Step-by-step explanation:
80 + 50m + 65 + 40m
90m+145
I only see one question.
The answer is the root 4 has the multiplicity of 2.
<span>4x^2 - 25
= (2x)^2 - 5^2 .................using a^2 - b^2 = (a+b)(a-b)
= (2x + 5)(2x - 5)</span>