Answer:
![\frac{3}{28}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B28%7D)
Step-by-step explanation:
Probability (P) is calculated as
P = ![\frac{requiredoutcome}{count}](https://tex.z-dn.net/?f=%5Cfrac%7Brequiredoutcome%7D%7Bcount%7D)
The first required outcome is a red sweet from a total of 3 + 5 = 8
P( red) = ![\frac{3}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B8%7D)
There are now 2 red left and a count of 7, since 1 has been eaten, thus
P( second red ) = ![\frac{2}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B7%7D)
P( red and red ) =
×
=
= ![\frac{3}{28}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B28%7D)
Dude I don’t feel like working
different between A and B
=30-(-30)
=60
position of C from A or B
=(60÷3)×2
=40
possible value of c
=-30+40
=10
possible value of c
=30-40
=-10
Answer:
![f'(x) = \frac{4x}{2x^2+1}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B4x%7D%7B2x%5E2%2B1%7D)
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]:
![f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2x%5E2%2B1%7D%20%5Ccdot%202%20%5Ccdot%202x%5E%7B2-1%7D)
- Simplify:
![f'(x) = \frac{1}{2x^2+1} \cdot 4x](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2x%5E2%2B1%7D%20%5Ccdot%204x)
- Multiply:
![f'(x) = \frac{4x}{2x^2+1}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B4x%7D%7B2x%5E2%2B1%7D)
<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:
c 15 square units
Step-by-step explanation:
it is very easy