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shtirl [24]
3 years ago
11

You want to make cylindrical containers of a given volume V using the least amount of construction material. The V

Mathematics
1 answer:
Rudik [331]3 years ago
4 0

Answer:

8/π

Step-by-step explanation:

Volume of the cylinder is:

V = πr²h

Surface area of the cylinder (with square top and bottom) is:

A = 2πrh + 8r²

Use the volume equation to write h in terms of r.

h = V / (πr²)

Substitute into the area equation:

A = 2V / r + 8r²

Take derivative with respect to r.

dA/dr = -2V / r² + 16r

Set to 0 and solve for r.

0 = -2V / r² + 16r

2V / r² = 16r

2V = 16r³

V = 8r³

Plug into the volume equation.

8r³ = πr²h

8r = πh

h / r = 8 / π

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I don't understand this
Charra [1.4K]
All the right triangles are similar.

x is the short side of the triangle with hypotenuse (2+8)=10.
x is the hypotenuse of the triangle with short side of length 2.

x/2 = 10/x . . . . ratio of hypotenuse to short side is the same for similar triangles
x^2 = 20 . . . . . multiply by 2x
x = √20 ≈ 4.47 . . . . . . . matches selection G
5 0
4 years ago
Easy points if u know it
Alchen [17]

Answer:

True

Step-by-step explanation:

The formula for the area of a circle is πr² where r is the radius. So if 3 is the radius, plug it into the formula:

π(3²)

Simplify it:

π(9)

This can be rewritten as:

9π

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7 0
3 years ago
Please answer quickly !!!
Dafna1 [17]
Dist from slide to fountain: 200 ft, because they are 2 grid spaces away from each other (y axis, coordinate (-2, 0) to coordinate (-2, -2))

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easy as 3.14159 (pi) xd
8 0
3 years ago
What is the conversion factor to convert cups to liters?
Gemiola [76]

Answer:

0.2365882365 L/cup

Step-by-step explanation:

The conversion factor can be found from the size of a cup in relation to a gallon, and the size of a cubic inch in relation to a liter.

1\,\text{cup}=8\,\text{fl oz}\times\dfrac{231\,in^{3}}{128\,\text{fl oz}}\times\left(\dfrac{0.254\,\text{dm}}{1\,\text{in}}\right)^{3}\times\dfrac{1\,L}{1\,dm^{3}}\\\\=\dfrac{8\cdot 231\cdot 0.254^{3}}{128}\,L=0.2365882365\,L

3 0
3 years ago
Which is greater? 79.47mi,54.28mi,65.5mi,98.43mi
Blababa [14]

Answer:

The greater value of the  given set is 98.43.

Explanation:

Here the units of the distance given for all the data is miles(mi).

So, the greater value is that value which has higher magnitude.

Values are 79.47,54.28,65.5 and 98.43

Values in their increasing order is given by

             54.28 < 65.5 < 79.47 < 98.43

 Values in their decreasing order is given by

             98.43 > 79.47 > 65.5 > 54.28

So, the greater value of the  given set is 98.43.

5 0
4 years ago
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