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-BARSIC- [3]
1 year ago
5

FAST. As part of a new advertising campaign, a beverage company wants to increase the dimensions of their cans by a multiple of

1.10. If the cans are currently 12 cm tall, 6 cm in diameter, and have a volume of 339.12 cm3, how much more will the new cans hold? Use 3.14 for π and round your answer to the nearest hundredth.
Mathematics
1 answer:
nalin [4]1 year ago
7 0
They will hold 112.25 cm^3 more. Find the volume of the second can with the new side lengths and subtract the orginal volume from the new one.
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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
Convert 0.70 hours to minutes. Round answers to the nearest tenth.
Dmitrij [34]

Answer:

B. 42 Mins

Step-by-step explanation:

you take .70x60mins and that is 42 mins.

3 0
3 years ago
______________ Angles have each of the pairs of opposite angles made by two intersecting lines *
myrzilka [38]

\huge \bf༆ Answer ༄

The Correct choice is B. Vertical

<u>V</u><u>ertical</u> Angles have each of the pairs of opposite angles made by two intersecting lines .

8 0
2 years ago
Read 2 more answers
Just started ratio, I need some help, please!
spayn [35]

Answer:

The answer would be B.

Step-by-step explanation: It is this answer because if it asks you 1 to 5, that means it is one, and then to 5.


Hope this answer helps!


6 0
3 years ago
Read 2 more answers
How many solutions does 3 - 2x = 5 - x + 3 + 4x have?
vitfil [10]

Well let's see.

3-2x=5-x+3+4x \\3-2x=8+3x \\-5x=5 \\x=-1 \\

The equation has exactly one solution.

Hope this helps.

5 0
3 years ago
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