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Sliva [168]
3 years ago
12

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m

m
Mathematics
1 answer:
daser333 [38]3 years ago
6 0

Answer:

\dfrac{dV}{dt}=502.65\ mm^3/s

Step-by-step explanation:

The volume of a sphere is given by :

V=\dfrac{4}{3}\pi r^3

The rate of change of volume means,

\dfrac{dV}{dt}=\dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r\times \dfrac{dr}{dt}

We have, \dfrac{dr}{dt}=2\ mm/s\ and\ r=40\ mm

So,

\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3\times 20\times 2\\\\=502.65\ mm^3/s

So, the volume is increasing at the rate of 502.65\ mm^3/s.

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The ratio of marbles to stones is 5 to 7 if there are 35 marbles how many stones is there?
icang [17]
5 : 7
Marbles : Stones

35/5 = 7
So stones
= 7 * 7
49

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3 0
3 years ago
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Your food costs are $5,500. Your total food sales are $11,000. What percent of your food sales do the food costs represent?
White raven [17]

Answer:

50

Step-by-step explanation:

5,500 is 50 percent of 11,000 :)

Hope This Helps.

4 0
3 years ago
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What is a formula for the nth term of a given sequence
IceJOKER [234]

Answer:

a_n=-12-4(n-1)

Step-by-step explanation:

The given sequence is

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The first term of this sequence is a_1=-12.

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d=-16--12

d=-16+12=-4

The nth term of this arithmetic sequence is;

a_n=a_1+d(n-1)

We substitute the values for the first term and the common difference to obtain;

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5 0
3 years ago
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Greek city-states began to form in 800 B.C. and in 200 A.D, Christians began getting persecuted. How many years passed between t
asambeis [7]

Answer: 1000 years

Step-by-step explanation:

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- up till 200 A.D i.e 200 years of After Christ disappearance

Hence, the number of years between the time that Greek city-states began to form and the persecution of Christians began is equal to the sum of years Greek city States started formation and Year persecution began

i.e 800 BC + 200 A.D = 1000 Years

Thus, the number of years of that passed was 1000 years

6 0
3 years ago
which values of x and y are solutions to the open sentence? 4y ≥ 3x 2 a. x = 3, y = 0 b. x = 4, y = 3 c. x = 6, y = 5 d. x = 7,
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4y ≥ 3x + 2

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