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3 years ago

Identify the y intercept of the line?

Mathematics

2 answers:

kotegsom [21]3 years ago

8 0

Answer:

B I hope this helped!

Step-by-step explanation:

allsm [11]3 years ago

8 0

Answer: (0,6)

Step-by-step explanation:

The y-intercept is where the line crosses the y-axis, so where x =0.

Here, the y-intercept is (0,6).

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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:

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

Learn more about integration here:

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5 0

2 years ago

Manas receives a commission of Rs.5,000 on sales of Rs.65,000.How much commission will he get on sales of Rs.20,000.

tangare [24]

$\\
\text{Let Manas receives a commission of Rs. 5000 on sales of Rs. 65000}\\
\\
\text{We need to find how much commision he will get on the sale of Rs.20000}\\
\\
\text{To find the commision, we use the unitary method.}\\
\\
\text{On sales of Rs. 65000, Manas receives a commision of}=5000\\
\\
\text{so on sales of Rs. 1, Manas will receiv a commision of}=\frac{5000}{65000}\\
\\
\text{Hence on sales of Rs. 20000, Manas will receiv a commision of}\\
\\=\frac{5000}{65000}\times 20000\\
\\
=1538.46$

Hence, on the sales of Rs. 20000, Manas will receive a commission of: Rs. 1538.46

6 0

3 years ago

HELP!! Determine the length of side CB.

bazaltina [42]

Answer:

3√2 is the answer as:

sin45°=p/b

1/√2= AC/CB

1/√2= 3/CB

cross multiplication

CB = 3√2

4 0

3 years ago

Can you put this into one sentence The Soviet team dominated the second period. The Americans scored twice in the last period. T

Greeley [361]

the americans scored twice in the last period although the soviet team dominated second period, after that the americans finally took the lead

(this is english not math change your question when you have to do this again)

4 0

3 years ago

Please help me out here, I’ve been reposting the same questions and have not seen people not answer mine. :( just please i will

anastassius [24]

Answer:

There are infinite solutions because they are the same equation

2D + 1G = 12

and

4D + 2G = 24 (divide by 2) 2D + G = 12

2D + 1G = 12 is the same as 2D + 1G = 12

3 0

3 years ago

Read 2 more answers