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3 years ago

Please Help!! Solve x2 = 121. A. 60.5 B. −11 C. 11 D. ±11

Mathematics

2 answers:

torisob [31]3 years ago

8 0

D is the right answer

mamaluj [8]3 years ago

6 0

D is the correct answer

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Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

3 0

3 years ago

To add 20.4 + 3.75 + 4.25, Crystal first added 3.75 and 4.25. Which property did Crystal use to add mentally?

evablogger [386]

Answer:

Associative Property of Addition

Step-by-step explanation:

From the list of given options, option A correctly answers the question and this is because

$a + b + c = a + (b + c)$ --- (1)

$a + b + c = (a + b) + c$ --- (2)

<em>The above illustrations only apply to Associative Property of Addition</em>

In Crystal's case:

$20.4 + 3.75 + 4.25 = 20.4 + (3.75 + 4.25)$

This can be compared to (1) above

Hence;

<em>Option A answers the question</em>

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3 years ago

Do you think there are more negative or positive aspects of using the Internet to get the news? Explain your answer.

Nady [450]

Answer:

64% of Americans say social media have a mostly negative effect on the way things are going in the U.S. today. Just one-in-ten Americans say social media sites have a mostly positive effect on the way things are going, and one-quarter say these platforms have a neither positive nor negative effect

Step-by-step explanation:

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2 years ago

Read 2 more answers

What is the answer to: -2x-y=-9

Nitella [24]

Y=9-2x, 9-2x=0, 2x=9, x=9/2, if you were asked to put it in standard form put down the first thing I said, if you were asked for solution then everything I said

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3 years ago

Two families go to a zoo.

ohaa [14]

Children ticket price=£9
Adult ticket price=£17
Let adult=A
Children=C
So, 2A+3C=61 (equation 1)
3A+5C=96(equation 2)
Multiply equation 1 by 3 and equation 2 by 2
Solve equations and get the answer.

5 0

3 years ago