3 years ago

What is the circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm?

1 answer:

6 0

If you can picture it , or sketch it. The diagonal of the rectangle (line connecting opposite corners) is the diameter of the circle. You can find the diagonal by using the Pythagorean theorem for a right triangle. The diagonal would be the hypotenuse.

10^2 + 24^2 = 676
sqrt(676) = 26

The formula for circumference is: diameter times pi.

C = 26pi

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The predicted cost c (in hundreds of thousands of dollars) for a company to remove p% of a chemical from its waste water is show

alukav5142 [94]

We presume your cost function is
c(p) = 124p/((10 +p)(100 -p))

This can be rewritten as
c(p) = (124/11)*(10/(100 -p) -1/(10 +p))

The average value of this function over the interval [50, 55] is given by the integral
$\frac{1}{55-50} \times \frac{-124}{11} \int\limits^{55}_{50} {(\frac{1}{x+10}+\frac{10}{x-100})} \, dx$
This evaluates to
(-124/55)*(ln(65/60)+10ln(45/50)) ≈ 2.19494

The average cost of removal of 50-55% of pollutants is about
$2.19 hundred thousand = $219,000