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3 years ago

Max is thinking of a double fact. It has a sum greater than 10 but less than 13. What number fact could it be?

Mathematics

1 answer:

igor_vitrenko [27]3 years ago

4 0

The answere would be 11 and 12

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Find integra of xlnxdx

Mademuasel [1]

Answer:

$\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

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

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

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

Increase the power by 1, then divide by the new power.

Given indefinite integral:

$\displaystyle \int x \ln x \:\: \text{d}x$

To integrate the given integral, use Integration by Parts:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\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}}$

$\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}$

$\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2$

Therefore:

$\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}$

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5 0

1 year ago

What is 6 1/4 x 3 3/5

aliya0001 [1]

Answer:

Step-by-step explanation:

Change mixed fraction to improper fraction. Then reduce to lowest term if possible.

6 1/4 x 3 3/5 = 25/4 * 18/5 = 25* 18 /4*5

= 5 * 18 / 4 {giving by 5th table}

= 5* 9 /2 { giving by 2nd tables}

= 45/2

8 0

2 years ago

How do I do this the easiest way?

Marina CMI [18]

Add the 3 item totals, then divide that number by 100, then, take that number and multiply by 9 (this gets the tax total). then you are going to want to add the total of the 3 items, and the tax amount, and you have your answer. do this with all the peoples items :)

4 0

2 years ago

Read 2 more answers

Solve for X: -22=-7+3/5x

stira [4]

solution for the problem-

X=-22

3 0

2 years ago

G(t)=2.0.4^t for t = -2

mafiozo [28]

Answer:

2(0.4)^-2 = 12.5

Step-by-step explanation:

do math noob

7 0

1 year ago