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MAVERICK [17]
3 years ago
12

Point Y is the circumcenter of triangle DEF.

Mathematics
2 answers:
lana66690 [7]3 years ago
8 0

Answer:

D

Step-by-step explanation:

Bingel [31]3 years ago
6 0

Answer:

Point Y is the center of the circle that passes through points D, E, and F.

Step-by-step explanation:

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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:

<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

brainly.com/question/27983581

brainly.com/question/27759474

5 0
2 years ago
When a rectangular pyramid is cut at an angle the cross section is a triangle. True or false
Fittoniya [83]

Answer:

True

Step-by-step explanation:

Think about it. you are cutting a rectangle in half. and when you put it in dimensions its still the same thing!

8 0
3 years ago
What are the different methods in finding the LCM​
Nezavi [6.7K]

Answer:

4 methods are there

Step-by-step explanation:

  1. Find the prime factorization of each number.
  2. Write each number as a product of primes, matching primes vertically when possible.
  3. Bring down the primes in each column.
  4. Multiply the factors to get the LCM.

please mark me as brainlist

8 0
3 years ago
Please help! will choose brainiest
SpyIntel [72]
X=0.84....................
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3 years ago
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