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STatiana [176]
3 years ago
8

Mr.brown can type 80 words in two minutes. how many words can he type in 40 minutes?

Mathematics
1 answer:
Anna11 [10]3 years ago
5 0

Answer:

1600

Step-by-step explanation:

We can setup a ratio in terms of words per minute.

Mr. Brown can type 80 words in 2 minutes, so our ratio looks like this:

40:2

In order to find how many words he can type in 40 minutes, we must set the minutes side of our ratio to 40. In order to do that, we must multiply our minutes side by a factor that makes it equal 40, and then multiply the words side by the same factor. We can divide 40 by 2 to figure out the factor, which is 20. Since the factor is 20, we must multiply it by the words side to figure out how many words he types in 40 minutes, which is 20 · 80 = 1600 words.

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2 years ago
A box with a square base and closed top is required to have a volume of 27,000 cm3
julia-pushkina [17]

Answer:

h=30cm

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Step-by-step explanation:

Let x be the dimension of the sides and h the dimension of height;

V=x^2h

#Material used is directly proportional to surface area. Minimizing surface area will minimize the amount of material used.

Area=2x^2+4xh

Find area as a function of x:

V=x^2h=27000\\\\h=\frac{27000}{x^2}\\\\Area=2x^2+4x(\frac{27000}{x^2})\\\\=2x^2+\frac{108000}{x}

To minimize Area, we find the first derivative of Area:

A=2x^2+\frac{108000}{x}\\\\A\prime=4x+\frac{108000}{x^2}=0\\\\\frac{4x^3-108000}{x^2}=0\\\\4x^3=108000\\\\x=30

#find the second derivative to verify the minimum:

A\prime=4x+\frac{108000}{x^2}\\A\prime\prime=4x+\frac{108000}{x^3}=124, x=30

Substitute x in the volume equation to find h:

h=\frac{27000}{x^2}\\\\=\frac{27000}{30^2}\\\\h=30

Hence, the dimensions of the box that minimize the amount of material used h=30cm and x=30cm

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Answer:

remember that it is a 90 angle. so that is the length because we know that a right angle adds to 90 degrees.

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