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Mathematics

1 answer:

erik [133]3 years ago

8 0

Answer:

Grades 6 and 8

Step-by-step explanation:

If the relationship of girls to boys in two different grades are proportional, they must have the same ratio. To tackle this problem, we can find the ratios of genders in each grade and compare them.

Step 1, finding ratios:

Finding ratios is just like simplifying fractions. We will reduce the numbers by their greatest common factors.

GRADE 6:

$9:12=\\3:4$

GRADE 7:

$12:18=\\2:3$

GRADE 8:

$15:20=\\3:4$

GRADE 9:

$25:36$

Can't be simplified!

Step 2:

Notice how grades 6 and 8 both had a ratio of 3:4. We can conclude that these two grades have a proportional relationship between girls and boys.

I hope this helps! Let me know if you have any questions :)

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Find the dimensions of a cylinder of volume 17 m3 of minimal cost if the top and bottom are made of material that costs twice as

Viefleur [7K]

Answer:

The answer is below

Step-by-step explanation:

The volume of the cylinder with radius (r) and height (h) is given as:

Volume = πr²h

17 = πr²h

h = 17 / πr²

Let k represent the cost of the side and 2k the cost of the bottom.

The area of the side = 2πrh, hence the cost of the side = k(2πrh)

The area of the top and bottom = 2πr², hence the cost of the top and bottom = 2k(2πr²)

The total cost (T) = cost of side + cost of the top and bottom

T = k(2πrh) + 2k(2πr²)

T = 2kπ(rh + 2r²)

Put h = 17/πr²

T = 2kπ (r×17/πr² + 2r²)

T = 2kπ(17/πr + 2r²)

The minimal cost is at dT/dr = 0

$\frac{dT}{dr} =0=\frac{d}{dr} [2k\pi(\frac{17}{\pi r} +2r^2)]\\\\4r-\frac{17}{\pi r^2} =0\\\\4r=\frac{17}{\pi r^2}\\\\r^3=\frac{17}{4\pi }=1.35\\\\r=\sqrt[3]{1.35}\\\\r=1.1\ m\\\\h=\frac{17}{\pi r^2} =\frac{17}{\pi (1.1)^2} \\\\h=4.42\ m$