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Gemiola [76]
3 years ago
11

Marc is half as old as Tony and three times as old as Ben. If the sum of their ages is 40, how old is Marc?

Mathematics
1 answer:
Murljashka [212]3 years ago
3 0

Answer:

Marc's age is 12

Step-by-step explanation:

Let

x ----> Marc's age

y ---> Tony's age

z ---> Ben's age

we know that

the sum of their ages is 40

so

x+y+z=40 -----> equation A

Marc is half as old as Tony

so

x=\frac{y}{2}

y=2x ----> equation B

Marc is three times as old as Ben

so

x=3z

z=\frac{x}{3} ----> equation C

substitute equation B and equation C in equation A

x+2x+\frac{x}{3}=40

solve for x

\frac{10x}{3}=40

x=40(3)/10\\x=12\ years

therefore

Marc's age is 12

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Answer:

The sharing cone holds about 9 times more popcorn than the skinny cone.

Step-by-step explanation:

The volume of a cone is given by the following formula:

V = \frac{\pi r^{2}h}{3}

In which r is the radius and h is the height.

Two cones:

Both have the same height.

The sharing-size cone has 3 times the radius of the skinny-size cone.

Skinny:

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V_{sk} = \frac{\pi r^{2}h}{3}

Sharing size:

radius 3r, height h. So

V_{sh} = \frac{\pi (3r)^{2}h}{3} = \frac{9\pi r^{2}h}{3} = 3\pi r^{2}h

About how many times more popcorn does the sharing cone hold than the skinny cone?

r = \frac{V_{sh}}{V_{sk}} = \frac{3\pi r^{2}h}{\frac{\pi r^{2}h}{3}} = \frac{3*3\pi r^{2}h}{\pi r^{2}h} = 9

The sharing cone holds about 9 times more popcorn than the skinny cone.

3 0
3 years ago
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Kobotan [32]

Answer:

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5 0
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Find the critical numbers of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne
NNADVOKAT [17]

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The critical values of a function f(x) are the values of x for which f'(x) = 0.

Given,

f(x) = \frac{x^{4} }{5(x-8)^{2} }

The derivative is found as follows, applying the quotient rule:

f'(x) = \frac{[5(x^{4} )(x-8)^{2}-5x^{4} [(x-8)^{2} ]' }{[5(x-8)^{2} ]^{2}  }

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The zeros of the function are the zeros of the numerator, thus:

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Answer:

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Step-by-step explanation:

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