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lesya [120]
3 years ago
7

The radius of a sphere is increasing at a rate of 3 mm/s. how fast is the volume of the sphere increasing when the diameter is 1

0 mm?
Mathematics
1 answer:
vredina [299]3 years ago
5 0

We will find the rate of change of volume with respect to the change of radius.


Volume, V(r) = (4/3) π r^3


Find rate of change of volume with respect to change of radius by differentiation


V'(r)=dV/dr = d[(4/3) π r^3]/dr = (4/3) π d[r^3]/dr =(4/3) π 3r^2


Therefore when diameter=10mm, r=5mm


V'(r)=V'(5)=(4/3) π (3(5^2))=(4/3) π 75 = 100 π mm^3/mm

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taurus [48]

Answer: The mean and standard deviation are 567.2 and 89.88 resp.

Step-by-step explanation:

Since we have given that

For 370 parts per million = 7% = 0.07

For 440 parts per million = 10% = 0.10

For 550 parts per million = 49% = 0.49

For 670 parts per million = 34% = 0.34

So, Mean of the carbon dioxide atmosphere for these trees would be

E[x]=370\times 0.07+440\times 0.1+550\times 0.49+670\times 0.34=567.2

And

E[x^2]=370^2\times 0.07+440^2\times 0.1+550^2\times 0.49+670^2\times 0.34=329794

So, Variance would be

Var\ x=E[x^2]-E[x]^2=329794-567.2^2=8078.16

So, the standard deviation would be

\sigma=\sqrt{8078.16}=89.88

Hence, the mean and standard deviation are 567.2 and 89.88 resp.

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4 years ago
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pshichka [43]

Approximate the real zeros of f(x) = x2 + 3x + 1 to the nearest tenth

<u>C. 2.6,-0.4</u>

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5 0
3 years ago
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the interior paint color melon madness,is 30% yellow, I used 72 ounces of yellow paint to mix the last batch. How many ounces of
Leona [35]
If the paint is 30% yellow, and you used 72 ounces of yellow, all you have to do is divide 72 by 30% to get the whole amount of ounces of paint made.
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So,

We can notice that the graph of g, is translated 2 units to the left and 4 units up. We can express these changes with the following equation:

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4 0
1 year ago
Ariel deposited 100$ into a bank account. Each Friday she will withdraw 10% of the money in the account to spend. Ariel thinks h
Scilla [17]
<span>Ariel deposited 100$ into a bank account. Each Friday she will withdraw 10% of the money in the account to spend. Ariel thinks her account will be empty after 10 withdrawals. Do you agree? Explain
OK, my initial answer is YES. I agree.
Why? Let me show you the solutions
=> 100 dollars = the money of Ariel in the bank
=> 10% = he withdraw every Friday
10% of 100 is:
=> 100 / 10 = 10 dollars
Thus,  after his 10th withdrawal, his account will be empty.</span>



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