The statement is true, but the inverse is false.
<span>The volume of a sphere is V = 4/3 x pi x r^3
The rind volume is the difference of two spheres. The radius of the inner sphere volume is, r - .1 r or .9 r. So the volume of the rind is
V = 4/3 x pi x r^3 - 4/3 x pi (.9 r )^3
V = 4/3 x pi x r^3 - 4/3 x pi x (.9^3) x r^3
Implicitly differentiating both sides with respect to t yields:
V' = ( 4 x pi x r^2 x r' ) - ( 4 x pi x (.9^3) x r^2 x r' )
This equation define the rate of change of the rind volume with respect to time.
As defined in the problem, r' = 2
As well, after 5 weeks the radius will be r = 2 * 5 = 10
V' = (4 x pi x 10^2 x 2) - (4 x pi x (.9^3) x 10 x 2)
V' = (800 x pi) - (800 x pi x (.729))
V' = (800 x pi) (1 - .729)
V' = (800 x pi)(.271)
V' = 681.09 cubic centimeters
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Answer:
It is 6.5 meters
The centimeter practical unit of length for many everyday measurements. A centimeter is equal to 0.01(or 1E-2) meter.
Hey, sorry this took so long for you to get an answer. Let me try.
<h2>Answers:</h2>
Part A: Answer choice C.
Part B: 6 people can come to the bowling alley.
<h2>Explanation:</h2>
For Part A, I've concluded that the answer is C. Ben can't spend more than $80, so it has to be equal to or less than 80. The flat fee is $45, and the cost per person is variable, $5.50p, so I combined all of those together and got <em>45+5.50p ≤ 80 .</em>
This is answer choice C.
And for Part B, I got 6. I got this answer from doing 80, the maximum cost, minus the flat rate, 45. Then, I divided this number by 5.50 to get the number of friends that could be paid for. I originally got 6.3636... but I rounded down because you can't have 0.3636... of a friend to come to the bowling alley.
Hopefully this isn't too late. Good luck.
