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1 year ago

1/2+1/9Please help me

Mathematics

1 answer:

musickatia [10]1 year ago

3 0

<em>If the fraction whose denominator are equal then they will add up</em>

In the given fraction 1/2 +1/9, the denominator of both the fraction 1/2 & 1/9 is not same

so, to make the base same we take the LCM of the 2 & 9

$\begin{gathered} \text{LCM of 2 \& 9 is 18} \\ Si,\text{ the fraction will be :} \\ \frac{1}{2}+\frac{1}{9}=\frac{9+2}{18} \\ \frac{1}{2}+\frac{1}{9}=\frac{11}{18} \end{gathered}$

Answer : 11/18

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The area of a square bedroom is 144 square feet. what is the length of one wall?

Rufina [12.5K]

The answer is: "12 feet" .
________________________________
Note: In a square, the length of EACH of the four sides of the square is the same.

Area = Length * width.

For a square, length = width.

So for a square, Area = length * width = (length of a side)² = s² ,

Given: A = s² = 144 ft² ;

Solve for the positive value of "s" .
________________________________
  → s² = 144 ft² ; Take the "square root" of each side ;

  → √(s²) = √(144 ft²) ;

  → s = 12 ft.
_______________________________
The answer is: 12 ft.
_______________________________

6 0

3 years ago

Can someone check whether its correct or no? this is supposed to be the steps in integration by parts

Gwar [14]

Answer:

$\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

Step-by-step explanation:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}$

Given integral:

$\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x$

$\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:$

$\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x$

Using <u>integration by parts</u>:

$\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

Therefore:

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}$

$\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:$

$\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}$

Therefore:

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

$\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:$

$\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}$

Divide both sides by 2:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}$

Rewrite in the same format as the given integral:

$\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

5 0

2 years ago

Reggie read a 400 page book. In 5 days .On the first day , he read 120 pages . each day after that , he read the same number. Of

forsale [732]

400x5 divided by 120

4 0

3 years ago

In terms of the number of moose, what is the relative frequency of male moose, female moose, adult moose, and baby moose? Write

user100 [1]

Answer:

I'm sorry is there a chart/graph, etc. to give us more information?

Without the added information there is no way for me to answer.

If you repost this question with a picture I would be more than happy to help.

6 0

3 years ago

Read 2 more answers

A loan officer makes $15 per hour working 2,000 hours each year. She also gets a fee of $35 for each loan she processes. If she

Afina-wow [57]

Answer:

$61,500

Step-by-step explanation:

For this problem, we will simply take her hourly wage and multiply that by the hours she worked and take her additional earnings for each loan processed and multiply that by the number of loans she processed.

Consider her hourly wage of $15 per hour. If she worked 2000 hours, then we can say she got paid ($15 * 2000) = $30000 for her work that year.

Consider her processing fee of $35 per loan processed. If she processed 900 loans, then we can say she got paid ($35 * 900) = $31500 for her processed loans that year.

Then, to find her yearly total earnings, we simply add those two values. $30000 + $31500 = $61500.

Thus the loan officer made $61500 that year.

Cheers.

7 0

3 years ago

Read 2 more answers