MATHEMATICS HIGH SCHOOL

The volume Equals Four thirds pi r cubed of a spherical balloon changes with the radius. a. At what rate (cubed/in) does the volume change with respect to the radius when r equals 9 in question mark b. Using the rate from part a, by approximately how much does the volume increase when the radius changes from 9 to 9.5 in question mark

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Given

Volume of spherical Balloon is given by

$V=(4)/(3)\pi r^3$

(a)Rate of change of balloon w.r.t to radius is given by

$\frac{\mathrm{d} V}{\mathrm{d} r}=3* (4)/(3)\pi r^2=4\pi r^2$

at $r=9\ in.$

$\frac{\mathrm{d} V}{\mathrm{d} r}=324\pi\ in.^2$

(b)Using the rate Volume change when radius increases from r=9 in. to r=9.5 in.

$\Delta V=4\pi (9)^2(9.5-9)=162\pi\ in.^3$

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If 3t-7 = 5t then 6t =How do I solve this? I've tried finding help online, but I'm getting more confused.

What is the answer to the following problem:
6÷2(1+2)=?

Answers

Hi, Soldier23!
6/2(1+2)
6/2(3)
6/2=3
3*3=9
I hope this helps;)

6/2(1+2)=9 Cuz 1+2=3 6/2=3 and 3X3=9!

Mike wants to make meatloaf. His recipe uses a total of 5 pounds of meat. If he uses a 3 to 1 ratio of beef to pork, how much pork will he use?

Answers

Ratio of beef to pork = 3 : 1

Beef:Pork = 3 : 1

Total ratio = 3 + 1 = 4

Amount of pork: Fraction of Pork = 1/4 of the whole meat

(1/4)*5 = 5/4 = 1.25

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Hope this explains it.

What is the square of 5y?

Answers

Answer:

25y^2

Step-by-step explanation:

$(5y)^2\n\n\mathrm{Apply\:exponent\:rule}:\quad \left(a*\:b\right)^n=a^nb^n\n\n\left(5y\right)^2=5^2y^2\n\n5^2=25\n\n=25y^2$

How do we do this problem 3(b3-5)

Answers

Well using the distributive property you get 3b3 - 15

3(b3-5)
=3b3-15

hope this helps

Last year, manuel saved $50 per month . this year, he increases his monthly savings by 25%. he plans to buy a smart phone for $375. at this rate, how long will it take him to save enough money to buy the smart phone if he starts saving for it this year?

Answers

First multiply 50 and .25 to find out how much extra he is saving, $12.5 Then add that to 50 to get $62.5. Divide $375 by $62.5 to get 6. It will take 6 months to save the money. Hope this helps!

Decide whether Rolle's theorem can be applied to f(x) = x2 + 5 on the interval [0, 3]. If Rolle's theorem can be applied, find all value(s) of c in the interval such that f '(c) = 0.

Answers

Answer:

Step-by-step explanation:

it is continuous in [0,3]

f'(x)=2x which exists in (0,3)

f(0)=0²+5=5

f(3)=3²+5=14

f(0)≠f(3)

so Rolle's theorem can't be applied.

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