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Alex Ar [27]
3 years ago
13

The sum of three numbers is 20. The second number is 4 times the first, and the sum of the first and the third is 8. Find the nu

mbers.
Mathematics
1 answer:
Digiron [165]3 years ago
8 0

Answer:

The numbers are 3, 12 and 5.

Step-by-step explanation:

Let the numbers =x, y and z.

The sum of three numbers is 20 implies x+y+z=20----------------i

The second number is 4 times the first implies y=4x--------------ii

The sum of the first and the third is 8 means x+z=8---------------iii

from (i), z=20-x-y---------iv

Put (iv) in (iii),

x+20-x-y=8

20-y=8

y=20-8=12

y=12

Put y=12 in (ii)

4x=y

x=y/4 = 12/4 = 3

x=3

Put x=3 and y=12 in (iv)

z=20-3-12=5

z=5

Therefore, the numbers are 3, 12 and 5.

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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

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

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the seventh grade class is putting on a variety show to raise money. it cost 700 dollars to rent the banquet hall that they are
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Answer:

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If $1000 as profit:

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ANSWER:

If need to raise atleast $1000 as income, they need to sell 67 tickets.

If need to raise atleast $1000 as profit, they need to sell 114 tickets.

The most probable answer would be 114 tickets

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