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zimovet [89]
3 years ago
6

Write each percent as a fraction in lowest terms.

Mathematics
1 answer:
Elina [12.6K]3 years ago
4 0

Answer:

Step-by-step explanation:

1) 15%=15/100=3/20

2) 36%=36/100=9/25

3) 44%=44/100=11/25

4) 45%=45/100=9/20

5) 8%=8/100=2/25

6) 60%=60/100=6/10=3/5

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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}

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

\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

5 0
2 years ago
A bank account appreciates at a rate if 0.05%
lidiya [134]

Answer:

if this is a true or false question it would be false...

Step-by-step explanation:

each bank has different fees and percentage rates, hope this helps

6 0
3 years ago
I need to know the correct answer
Fantom [35]
Well since 1 tone is 2,000 pounds so you will do 7 times 2,000 which equals 
14,000 pounds.
7 0
4 years ago
Read 2 more answers
Help!!!! How do u do #13
alisha [4.7K]
The answer is 288cm 

Hope this helps!


7 0
3 years ago
Read 2 more answers
Help me!! I need the answer quick!
alukav5142 [94]

Answer:

A

Step-by-step explanation:

b*h*1/2

8*5.5*1/2

=22

6 0
2 years ago
Read 2 more answers
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