The radius r(t)r(t)r, (, t, )of a sphere is increasing at a rate of 7.57.57, point, 5 meters per minute. at a certain instant t_0t 0 t, start subscript, 0, end subscript, the radius is 555 meters. what is the rate of change of the surface area s(t)s(t)s, (, t, )of the sphere at that instant?

ds/dt=69743.35m^2/min

Step-by-step explanation:

The radius r(t)r(t)r, (, t, )of a sphere is increasing at a rate of 7.57.57, point, 5 meters per minute. At a certain instant t_0t 0 t, start subscript, 0, end subscript, the radius is 555 meters. What is the rate of change of the surface area S(t)S(t)S, (, t, )of the sphere at that instant?

If i could understand the question correctly, the typos notwithstanding

r=radius, 555m

dr/dt=rate of change in radius 5m/min

ds/dt=rate of change in surface area   ?

S=area of a sphere 4

ds/dt=ds/dr*dr/dt.................................1

ds/dr=differentiation of the area of a sphere=

ds/dt=*5

ds/dt=69743.35m^2/min

The surface area of the sphere will change by 69733.35 square meters for every minute.

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step by step resolutions

1) n+n+1+n+2=51

3n+3=51

3n=48

n=16

the three numbers are 16, 17 and 18.

2) x+15=4x

3x=15

x=5

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3) the two digits are x and y.

y=3x

(10x+y)+(10y+x)=88

y=3x

11x+11y=88

y=3x

x+y=8

x+3x=8

x=2

the original number can be either 28 or 82.

4) n+(n+2)+(n+4)=48

3n+6=48

3n=42

n=14

the numbers are 14, 16 and 18.

5) y=x+3

10y+x+10x+y=143

y=x+3

11x+11y=143

y=x+3

x+y=13

x+x+3=13

2x=10

x=5

the original number can be 57 or 75.

hope this !