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Alex
3 years ago
12

Tammy earns 45 dollars per week working part time at a book store. She makes one dollar more for each book that she sells. The a

mount, A(in dollars), that Tammy earns in a week If she sells b books is given by the following function
How much does Tammy earn in a week if she sells 32 books?
Mathematics
1 answer:
seraphim [82]3 years ago
3 0

 Answer

77

  Step-by-step explanation:

You add how much she earns a week with 32 because she earns $1 dollar per book.

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Evaluate the following integral (Calculus 2) Please provide step by step explanation!
Step2247 [10]

Answer:

\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=-\dfrac{2}{x+1}+\text{C}

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a <u>constant of integration</u>.

<u>Given integral</u>:

\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x

Factor the denominator:

\begin{aligned}\implies x^2+2x+1 & = x^2+x+x+1\\& = x(x+1)+1(x+1)\\& =  (x+1)(x+1)\\& =  (x+1)^2\end{aligned}

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\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}

\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int 2(x+1)^{-2}\:\:\text{d}x

\boxed{\begin{minipage}{4 cm}\underline{Integrating $ax^n$}\\\\$\displaystyle \int ax^n\:\text{d}x=\dfrac{ax^{n+1}}{n+1}+\text{C}$\end{minipage}}

Use <u>Integration by Substitution</u>:

\textsf{Let }u=(x+1) \implies \dfrac{\text{d}u}{\text{d}x}=1 \implies \text{d}x=\text{d}u}

Therefore:

\begin{aligned}\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x & = \int 2(x+1)^{-2}\:\:\text{d}x\\\\& = \int 2u^{-2}\:\:\text{d}u\\\\& = \dfrac{2}{-1}u^{-2+1}+\text{C}\\\\& = -2u^{-1}+\text{C}\\\\& = -\dfrac{2}{u}+\text{C}\\\\& = -\dfrac{2}{x+1}+\text{C}\end{aligned}

Learn more about integration here:

brainly.com/question/27988986

brainly.com/question/27805589

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3 years ago
Given ZW=20. Answer the questions please. ​
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