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Akimi4 [234]
3 years ago
10

Which is the approximate circumference of a circle with a diameter of 60 cm?

Mathematics
1 answer:
Dima020 [189]3 years ago
8 0
The circumference is the diameter times pi.

d=60 \ [cm] \\ \\
C=60\pi \approx 60 \times 3.14=188.4 \approx 188 \ [cm]

The answer is D.
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The next part of the question asks to maximize this result - our target function which we'll call g(a,b,c)=3abc(10-a) - subject to 0\le a,b,c\le12.

We can see that g is quadratic in a, so let's complete the square.

g(a,b,c)=-3bc(a^2-10a+25-25)=3bc(25-(a-5)^2)

Since b,c are non-negative, it stands to reason that the total product will be maximized if a-5 vanishes because 25-(a-5)^2 is a parabola with its vertex (a maximum) at (5, 25). Setting a=5, it's clear that the maximum of g will then be attained when b,c are largest, so the largest flux will be attained at (a,b,c)=(5,12,12), which gives a flux of 10,800.
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