Answer:

General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:

Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
Integration Rule [Reverse Power Rule]:

Integration Property [Multiplied Constant]:

Integration Methods: U-Substitution
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify given.</em>

<u>Step 2: Integrate Pt. 1</u>
<em>Identify variables for u-substitution</em>.
- Set <em>u</em>:

- [<em>u</em>] Differentiate [Derivative Rules and Properties]:

<u>Step 3: Integrate Pt. 2</u>
- [Integral] Rewrite [Integration Property - Multiplied Constant]:

- [Integral] Apply Integration Method [U-Substitution]:

- [Integral] Apply Exponential Integration:

- [<em>u</em>] Back-substitute:

∴ we have used substitution to <em>evaluate</em> the indefinite integral.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Arcsin[tan(π/4)]
1st calculate tan(π/4)
tan(π/4) = tan(45°) = 1
Now plug this value in the original equation:
arcsin(1) = 90° or arcsin(1) = π/2
Answer:
There were 118,637 personal care aides in 2014.
Step-by-step explanation:
By 2024, there will be a need for 160,328 personal care aides, a growth of about 26% over 2014 levels.
This means that the 2014 levels is 100% - 26% = 74% of the 2024 levels.
Number of personal care aides in 2014:
74% of 160,320. So
0.74*160320 = 118,637
There were 118,637 personal care aides in 2014.
Answer:

Step-by-step explanation:

Do cross multiplication


Divide both sides by 12

Calculate

Hope I helped!
Best regards! :D
Answer:
357.77088
Step-by-step explanation:
the answer is in the attached image