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Verizon [17]
4 years ago
9

3.) A glass of water is being filled up slowly. It initially starts out with 4

Mathematics
1 answer:
maria [59]4 years ago
4 0

Answer:

  8 minutes

Step-by-step explanation:

The amount in the glass after m minutes can be described by ...

  a = 4 + 3/2m

We want to find m when a=16, so ...

  16 = 4 + 3/2m

  12 = 3/2m . . . . . subtract 4

  8 = m . . . . . . . . . multiply by 2/3

It will take 8 minutes to fill the glass.

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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

Base sides, x=30cm

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

8 0
4 years ago
The area of a rectangle is 45.5 square inches the base of the rectangle is 7 inches what is the height of the rectangle in inche
icang [17]

Answer:

A=45.5B= 7 inches therefore: 45.5/7= 6.5height is 6.5.

Step-by-step explanation:

5 0
3 years ago
I need help with this answer please
Elis [28]

Answer:

Y= x+2

Step-by-step explanation:

The x value is always adding 2 to get the y value

1+2=3

2+2=4

3+2=5

4+2=6

5+2=7

Therefore your answer is y = x + 2

Hope this helps!

5 0
4 years ago
Read 2 more answers
How to decrease 64 by 60%
Fofino [41]
To decrease 64 by 60%
Working Out:

60%/100% = 0.6
0.6 x 64 = 38.4

Therefore to decrease by 60%

64 - 38.4 = 25.6

:)
8 0
3 years ago
2. A large rectangular swimming pool is 1,000 feet long, 100 feet wide, and 10 feet deep. The pool is filled to the top with wat
RideAnS [48]

Answer:

a) 100000 feet

b) 1000000 feet

c) 10^5 and 10^6

Step-by-step explanation:

a) to find area, the formula is length x width

therefore, you would calculate 1000 x 100.

b) to find volume, the formula is length x width x height

therefore you would calculate, 1000 x 100 x 10.

c) look at the amount of zeros for each number and you will find your answer.

Hope this helps!!

8 0
2 years ago
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