<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
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
</span>
To simplify the expression we are going to use the distributive property of multiplication:
.
We can infer from our problem that
,
, and
. So lets apply the property to simplify our expression:
We can conclude that the correct answer is <span>
-8x3 + 6x2</span>
Answer:
99
Step-by-step explanation:
1/9 of 72 = 8
1/4 of 72 = 18
1 + 8 = 9
72 + 18 = 90
90 + 9 = 99
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
Answer:
-4, -3, 0, 2
Step-by-step explanation:
Rewrite each given equation as
where each of the last equalities follows from the change-of-base identity,
for any base <em>b</em> > 0 and <em>b</em> ≠ 1. I picked the natural base, <em>e</em>.
Then
as required.