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Morgarella [4.7K]
3 years ago
10

For the solid described below, find the dimensions giving the minimum surface area, given that the volume is 64 cm3. a closed cy

linder with radius r cm and height h cm.
Mathematics
1 answer:
stepladder [879]3 years ago
8 0
The volume of the cylinder is:
 V = pi * r ^ 2 * h = 64
 The surface area is:
 A = 2 * pi * r ^ 2 + 2 * pi * r * h
 We write the area as a function of r:
 A (r) = 2 * pi * r ^ 2 + 2 * pi * r * (64 / (pi * r ^ 2))
 Rewriting:
 A (r) = 2 * pi * r ^ 2 + 2 * (64 / r)
 A (r) = 2 * pi * r ^ 2 + 128 / r
 Deriving:
 A '(r) = 4 * pi * r - 128 / r ^ 2
 We equal zero and clear r:
 0 = 4 * pi * r - 128 / r ^ 2
 128 / r ^ 2 = 4 * pi * r
 r ^ 3 = 128 / (4 * pi)
 r = (128 / (4 * pi)) ^ (1/3)
 r = 2.17 cm
 The height is:
 h = 64 / (pi * r ^ 2)
 h = 64 / (pi * (2.17) ^ 2)
 h = 4.33 cm
 Answer:
 
The dimensions giving the minimum surface area are:
 
r = 2.17 cm
 
h = 4.33 cm
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Yes it is possible that a population of Norway rats carries a different genetic mutation than a population of same rats in other regions because occasionally, environmental factors of a certain area can cause the population of a region to undergo mutation .

<h3>What is the population mutation?</h3>

A mutation is defined as a change in the DNA or genetic sequence of an organism that can significantly affect or not affect the function of a specific gene in organism.

Now, we can say that it is possible that a population of Norway rats carries a different genetic mutation than a population of same rats in other regions because occasionally, environmental factors (such as exposure to harsh UV Rays) of a certain area can cause the population of a region to undergo mutation whereas the other population doesn't contain that mutation.

This environmental factor above will cause a slight change in the genetic makeup of the population of rats of Northern America. However, if the changes in genetic makeup continues to happen in North American Norway rats, a time will come when they will be genetically different from same rats in Norway or other regions by  being a different specie in a phenomenon that is called speciation.

Read more about Mutations at; brainly.com/question/17031191

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1 year ago
I don’t understand this at all helppp
Fynjy0 [20]

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5^2 + 8^2 should equal 12^2 for it to be a right triangle.

8 0
3 years ago
What is the median for 44 48 50 and 65
AlexFokin [52]

Answer:

Step-by-step explanation:

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In a race between 18 people, how many ways can the top 5 finishers be arranged?
snow_lady [41]

Answer:

Step-by-step explanation:

This is permutation, since order matters.  The formula for us is

₁₈P₅ = \frac{18!}{(18-5)!} which simplifies to

₁₈P₅ = \frac{18*17*16*15*14*13!}{13!}

The factorial of 13 cancels out on the top and bottom leaving you with

₁₈P₅ = 18 × 17 × 16 × 15 × 14

which comes to 1,028,160 ways

Another way to look at it is:  the first 5 people of 18 finish and the others you don't care about.  Once the first place person is first, there are only 4 of the 18 left to finish in second place.  Then there are only 3 left to finish in third place, etc.  So if we use that reasoning, we don't even need to use the formula, we can just say

18 * 17 * 16 * 15 * 14 and those are the first 5 people of 18 to finish.

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4 years ago
The height of a poplar tree in feet at age t years can be modeled by the function h(t)=6+3ln(t+1) . use the model to predict the
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When the height is 18 feet, we have:

6+3ln(t+1) = 18

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Divide both sides by 3

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Take the exponent of both sides

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t + 1 = 54.6

Subtract 1 from both sides

t = 53.6

This means that the height of the tree will exceed 18 feet after 53.6 years

Read more about logarithmic functions at:

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