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3 years ago

5-6x.8571 = 8x8571 + 17

Mathematics

1 answer:

disa [49]3 years ago

6 0

false

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

Resolber la siguientes problemas

german

Lo siento, no hago matemáticas por favor hazlo tú mismo. En caso de que no traduzcas esto voy a poner un par de números. 34 es el número para hacer que alguien que habla inglés esto es legítimo. 45 = 28 + x28. Te quiero

3 0

2 years ago

(6x - 12)/3 + 4 = 18/x

svet-max [94.6K]

X=3
X=-3
Hope this help!

3 0

2 years ago

If your mom only has half a gallon left will she make it to the nearest gas station 26 miles away

Svetach [21]

Answer:

Depends how much is half a gallon in her car

usally a car has 100+ space for gallons

if she has any less than 50 gallons max

she won’t make it

so she probley will if she has more than 26 gallons of gas at half a tank

7 0

2 years ago

On average, Mackenzie drinks of an 8-ounce glass of water in 24 hours. How much

vichka [17]

Answer:

1/3

Step-by-step explanation:

If Mackenzie drinks 8 ounces of water per 24 hours, that could be written as a ratio and a fraction. 8:24, 8/24

8/24 in its simplest form is 1/3.

3 0

2 years ago