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Rzqust [24]
3 years ago
11

I need help on 18, thank you!

Mathematics
1 answer:
adelina 88 [10]3 years ago
5 0
I think the answers are: a = 60°, b = 45°, c = 36°.
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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
3 years ago
Identify the double displacement reaction.
Anit [1.1K]
A double replacement reaction occurs when the ionic parts of two ionic compounds are exchanged. 

Reaction 1 results in a product which is a single compound. No ionic parts are exchanged. 

Reaction 3 results in one compound being separated into its elemental parts. No ionic parts are exchanged. 

Reaction 4 has two reactants, but Pb is an element and not an ionic compound. No ionic parts are exchanged. 

Hence, the answer is Reaction 2. Both NaBr and Ca(OH)2 are ionic compounds. Br - is the anion in NaBr, and (OH)2 is also an anion. Ionic parts are exchanged. 
3 0
3 years ago
In order to solve for the variable in the equation 2 (4 x + 3) + 4 = 3 x minus (2 x + 4), Giovanni first applies the distributiv
Alenkinab [10]

Answer:

8x + 6 + 4 = 3x - (2x + 4)

Step-by-step explanation:

When Gio applies the distributive property, the equation above is the result. Naturally, I look at the 1st parenthesis I see and start the 1st distributive property there first. The 2nd distributive property would be the other parenthesis where you multiply by -1, so you would get 8x + 6 + 4 = 3x - 2x - 4

5 0
3 years ago
Read 2 more answers
A copy machine can print 480 copies every 4 minutes.
Elenna [48]
And what’s the question?????
5 0
3 years ago
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A quadrilateral is graphed on a coordinate plane. If the vertices are A(2, 6), B(6, 0), C(2, –6) and D(–4, 0), which two points
Alik [6]

Check the picture below.

6 0
4 years ago
Read 2 more answers
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