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3 years ago

In an indirect proof, it is essential to reach a _____of a known fact.

Mathematics

2 answers:

Sonbull [250]3 years ago

8 0

Answer: 2. conclusion

alexandr402 [8]3 years ago

4 0

Answer: 3. contradiction

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Find the volume of the solid formed by revolving the region bounded by LaTeX: y = \sqrt{x} y = x and the lines LaTeX: y = 1 y =

Strike441 [17]

Answer:

The volume is:

$\displaystyle\frac{37\pi}{10}$

Step-by-step explanation:

See the sketch of the region in the attached graph.

We set the integral using washer method:

$\displaystyle\int_a^b\pi r^2dx$

Notice here the radius of the washer is the difference of the given curves:

$x-\sqrt{x}$

So the integral becomes:

$\displaystyle\int_1^4\pi(x-\sqrt{x})^2dx$

We solve it:

Factor $\pi$ out and distribute the exponent (you can use FOIL):

$\displaystyle\pi\int_1^4x^2-2x\sqrt{x}+x\,dx$

Notice: $x\sqrt{x}=x\cdot x^{1/2}=x^{3/2}$

So the integral becomes:

$\displaystyle\pi\int_1^4x^2-2x^{3/2}+x\,dx$

Then using the basic rule to evaluate the integral:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{2x^{5/2}}{5/2}+\frac{x^2}{2}\right|_1^4$

Simplifying a bit:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{4x^{5/2}}{5}+\frac{x^2}{2}\right|_1^4$

Then plugging the limits of the integral:

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Taking the root (rational exponents):

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Then doing those arithmetic computations we get:

$\displaystyle\frac{37\pi}{10}$

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3 years ago

Which following fractions is equivalent to 0.45

vladimir1956 [14]

0,45= $\frac{45}{100} =\frac{9}{20}$

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3 years ago

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There is a sequence of rigid transformations that takes A to A', B to B', and C to "

Marina CMI [18]

Answer:

I think it's D

Step-by-step explanation:

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3 years ago

Target sells 24 bottles of water for $3, and 36 bottles of water for $4. Which is the better buy and by how much?

quester [9]

24 bottles @ $3 = 8 bottles per dollar
12.5 cents per bottle

36 bottles @ $4 = 9 bottles per dollar
11.1 cents per bottle

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3 years ago

Mrs.Carle returned 10 books to the library. When she looked back in her classroom,she now had 88 books. Write an algebraic equat

Nata [24]

The algebraic equation is 10 + x= 88

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3 years ago

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