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givi [52]
3 years ago
14

I need this answered asap please and thankyou :D

Mathematics
1 answer:
suter [353]3 years ago
5 0

Answer:

b

Step-by-step explanation:

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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
2 years ago
Plz help me get the right answer ASAP please
Ierofanga [76]
<h2>Greetings!</h2><h3>When expanding brackets, you simply multiply whatever is inside the brackets by what is outside:</h3>

(7x * x) + (7x * 20)

<h3>Which would result in the answer being:</h3>

7x^{2} + 140x


<h2>Hope this helps!</h2>
5 0
3 years ago
Read 2 more answers
3 + 10.8 is:<br> rational<br> irrational<br> Idk what this is if u could please help me
ratelena [41]

Answer:

3 + 10.8 is : rational.

Step-by-step explanation:

the reason for this is because it is neither a variable, pi, or numbers like square root 2.

4 0
2 years ago
Need help ASAP!!!!!!!!
egoroff_w [7]

Answer:

24/35

Step-by-step explanation:

8 0
2 years ago
Two friends argue about the calculated probability of flipping a coin to show heads three times in a row. steve mentions that ea
den301095 [7]

Solution:

A coin is flipped three times,resulting three heads in a row.

Since Steve has mentioned that ,  each flip  of a coin is unconnected to the previous flip.

Two or more events are said to be independent if occurrence of one of them is not affected by the Occurrence of other.

This is an example of independent events.

In terms of probability, P (A∩B∩C)= P(A)×P(B)×P(C)

4 0
3 years ago
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