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2 years ago

Please assist me with this problem

Mathematics

1 answer:

Anna11 [10]2 years ago

8 0

Answer:

Option B is not a justification

Step-by-step explanation:

Option A is a justification (to get two pair of similar triangles (ABC-ACD) and (ABC-BCD))

Option C is a justification (a^2 = cy, b^2 = cx, a^2 + b^2 = cy + cx)

Option D is a justification (a^2 + b^2 = cy + cx = c(y + x) = c^2)

=> Option B is not a justification

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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:

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

6 0

2 years ago

How do i solve for x

sergiy2304 [10]

Expplanation and Answer:

y=mx−7

Swap sides so that all variable terms are on the left hand side.

mx−7=y

Add 7 to both sides.

mx=y+7

Divide both sides by m.

y+7

Dividing by m undoes the multiplication by m.

y+7

3 0

2 years ago

6/5 ÷ ____ = 6 A. 1/5 B. 30 C. 1/30 D. 5

murzikaleks [220]

Answer:

A. $\displaystyle \frac{1}{5}$

Step-by-step explanation:

$\displaystyle \frac{6}{5} \div \frac{1}{5} = 6 \\ \\ OR \\ \\ \frac{6}{5} \div 6 = \frac{1}{5}$

I am joyous to assist you anytime.

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2 years ago

How long is the base of a parallelogram if it has an area of 120 square inches and a height of 10 square inches?

nataly862011 [7]

Answer:

Your answer should be 1,200 because 120 x 10 is 1,200

5 0

2 years ago

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2. make sure you show all your work for full points. what is z?

LenKa [72]

Answer:

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1 year ago