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svetoff [14.1K]
2 years ago
12

Simplify (ab²)²4a²/2a³​

Mathematics
1 answer:
Vanyuwa [196]2 years ago
6 0

Answer: 4ab   1a

Step-by-step explanation:

(2ab)² 4a² / 2a³​

4ab  8a / 8a

8a / 8a

4ab   1a

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Melinda has shown that a function, f(x), increases by 4 for every unit in the domain. What does this prove?
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It proves The function f(x) is an arithmetic sequence.
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3 years ago
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The lengths of two sides of a triangle are 5 and
Gwar [14]

Answer:

D) 2

Step-by-step explanation:

A Triangle two sides added together must always be greater than the other side.

It can not be 2 because the two sides of a triangle added are not greater than the other side.

Here 5 + 2 = 7 which is not greater than 7 on the other side, so 2 fails.

5 0
2 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:

<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>.

\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 <u>indefinite integral</u>:

\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
What is the prime factorization of 24
xxMikexx [17]

Answer:The prime factorization is the product of the circled primes. So the

prime factorization of 24 is 24 = 2 · 2 · 2 · 3 = 3.

Step-by-step explanation:

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In the isosceles trapezoid LMNO, find the value of x.
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Answer:

15 would be the correct answrr

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