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2 years ago

What is the answer for #7?

Mathematics

1 answer:

Karo-lina-s [1.5K]2 years ago

3 0

Answer:

radius: 1.84 in
height: 3.68 in

Step-by-step explanation:

After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...

V = πr²·h = 2πr³ = 39 in³

Then the radius is ...

r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in

h = 2r = 3.67557 in ≈ 3.68 in

_____

The total surface area of a cylinder is ...

S = 2πr² + 2πrh

For a given volume, V, this becomes ...

S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r

The derivative of this with respect to r is ...

S' = 4πr -2V/r²

Setting this to zero and multiplying by r²/2 gives ...

0 = 2πr³ -V

r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r

If we substitute the equation for V into the equation just above this last one, we have ...

0 = 2πr³ - πr²·h

Dividing by πr² gives ...

0 = 2r - h

h = 2r . . . . . generic solution for cylinder optimization problems

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Rama09 [41]

Answer:

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Step-by-step explanation:

The equation given are

$f(x) \to 250$

and $g(x) \to 0$

with $g(x) > 0 \ as\ x ---> 5$

The objective is to obtain

$\lim_{x \to 5} \frac{f(x)}{g(x)}$

This mathematically evaluated as

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2 years ago

Write the equation of a line with a slope of O and a y-intercept of -2. Do not use spaces

Salsk061 [2.6K]

<h3>Answer: y = -2</h3>

================================================

Work Shown:

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y = mx+b

y = 0x+(-2)

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y = -2

This line is horizontal and goes through -2 on the y axis.

Two points on this line are (0,-2) and (1,-2)

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2 years ago

The digit in the tens placeof a two digit is three times that in the units place. if the digits are reversed , the new no will b

Charra [1.4K]

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Obviously, inverting the digits would lead to the number $10y+x$ .

Since this new number is 36 less than the original, we have

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Since we also know that the digit in the tens place is three times that in the units place, we can add an equation to form a system:

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3 years ago

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enyata [817]

Answer:

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Step-by-step explanation:

* Lets revise the volume of the sphere

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- Mass is the weight and volume is the size, so density is weight

divided through size

- Density = weight ÷ volume

* Now lets solve the problem

∵ The clay's density ≅ 88 pounds/cubic foot

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8 0

3 years ago

Help ! With step by step solution

nirvana33 [79]

Answer:

the correct answer is C

Step-by-step explanation:

first step you change the x and y powers to the square root(showing in the pic).

second the number outside of the parenthesis times the numbers inside the parenthesis and then you just figure it out how it works...

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