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3 years ago

Which unit is the best for measuring the distance between two cities?

Mathematics

2 answers:

mrs_skeptik [129]3 years ago

7 0

Answer:

kilometer

Step-by-step explanation:

OleMash [197]3 years ago

7 0

The best unit for measuring the distance between two cities is kilometer.

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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

2 years ago

The 4 problems distributive property thanks

n200080 [17]

Looks like all you have to do it multiply the numbers together; there is no application of the Distributive Property to these problems.

7 0

2 years ago

Help I would love to give you a thanks

WARRIOR [948]

Answer:

Formula

Step-by-step explanation:

7 0

2 years ago

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What is equation of a line that is parallel to y = -6x – 1 and passes through the point (1,4)

Akimi4 [234]

Answer:

y = -6x + 10

Step-by-step explanation:

Parallel lines share the same slope. Given y = -6x – 1, we know that the equation of this new line has the form y = -6x – C. The coordinates of the point (1, 4) determine the value of C:

(4) = -6(1) – C, or:

4 = -6 - C

Then C = -10, and the desired equation is

y = -6x – (-10), or

y = -6x + 10

5 0

2 years ago

Which equation is false?

aivan3 [116]

C is false. 9 multiplied by 7 equals 63.

7 0

2 years ago

Read 2 more answers