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bazaltina [42]
4 years ago
7

Determine which side is the smallest in the diagram

Mathematics
1 answer:
AnnyKZ [126]4 years ago
5 0

the shortest side is always opposite the smallest angle.

In triangle ABC the shortest side is AC

In triangle ADC  the shortest side is DC

DC<AC since they are in the same triangle.

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Integrate x+1/sqrt(x). I know that the answer is 2/3 • sqrt(x) • (x+3) + C, but I don't know how it is simplified from 2/3 • x^3
Andreas93 [3]

\displaystyle\int\frac{x+1}{\sqrt x}\,\mathrm dx=\int\frac x{x^{1/2}}+\frac1{x^{1/2}}\,\mathrm dx

=\displaystyle\int x^{1/2}+x^{-1/2}\,\mathrm dx

By the power rule,

=\dfrac{x^{3/2}}{\frac32}+\dfrac{x^{1/2}}{\frac12}+C

(this seems to be the step you're not getting?)

=\dfrac23x^{3/2}+2x^{1/2}+C

The next step is to pull out a common factor of x^{1/2} from the antiderivative:

x^{3/2}=x^{1/2+1}=x^{1/2}\cdot x^1

so that the final result is

\dfrac23x^{3/2}+2x^{1/2}+C=\dfrac23x^{1/2}(x+3)+C

3 0
3 years ago
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babunello [35]
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8 0
4 years ago
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What's the area please
mezya [45]

Answer:

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I guess this may help you

8 0
3 years ago
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Find the equivalent expression 3p + 12m + 8
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Answer:

3(p+4m) + 8

Step-by-step explanation:

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3 years ago
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lilavasa [31]

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