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2 years ago

Trevor paints 1/6 of the fence surrounding his farm each day how many days will it take him to paint 3/4 fence?

Mathematics

1 answer:

scZoUnD [109]2 years ago

7 0

Find common denominators (12) and multiply the numerators and subtract. the answer is 7/12

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How many permutations of the letters ANSWER end in a vowel?

GREYUIT [131]

Update the question so it's on-topic for Mathematics Stack Exchange. Closed 4 years ago. How many words can be made by using the letters of the word ENGLAND such that words begin and end with a vowel? I couldn't understand how come the answer to this question is 120

6 0

3 years ago

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:

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

Learn more about integration here:

brainly.com/question/27805589

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brainly.com/question/27759474

5 0

2 years ago

Find the surface area of the sphere with the given dimension. Leave your answer in terms of pi

AfilCa [17]

A you just divide bro

5 0

2 years ago

(06.06 MC) The work of a student to find the dimensions of a rectangle of area 8 + 12x and width 4 is shown below:

zheka24 [161]

Answer:

step 2

Step-by-step explanation:

theres a one in front of the () meaning it should have look like this

4+4x+2

7 0

2 years ago

8.4 gallons of gas for $23.94. Which equation can be used to determine the price of each gallon of gas?

mojhsa [17]

Here is the equation: (gas=g)

8.5g= 23.94

All you need to do is the inverse of multiplication on the other side. (division)

23.94/8.5= 2.81647.....

g= 2.82 (rounded to the hundredths place)

I hope this helps!
~kaikers

6 0

3 years ago