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3 years ago

Choose the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1).

Mathematics

1 answer:

Bond [772]3 years ago

3 0

The answer to the question is d

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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,

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

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3 years ago

What is the difference of 15 and 7?<br> O<br> 3<br> Sondrit<br> Not

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Answer:

Step-by-step explanation:

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3 years ago

PLEASE HELP I NEED THE VALUES OF M AND P!!!!!!!! WILL GIVE BRAINLIST!!!!

ki77a [65]

Answer:

m=5 and p=4

Step-by-step explanation:

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A large bag of marbles contains red (R) and blue (B) marbles. Marbles are pulled one at a time, recorded, and placed back in the

ehidna [41]

The answer will be A.

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Suppose you want to factor the expression x2+ 2xn+n2. Given that n> 0, what are the factors? Explain.

spin [16.1K]

Answer:

(x + n)^2

Step-by-step explanation:

Okay! Let's get this going!

(x + n ) ^2 is correct because first we get

x^2 and n^2. Yet we need to add one more part to this to make it true which is x * n. We multiply this by two since according to the formula (a + b)^2 = a^2 + 2ab + b^2

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3 years ago

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