Amachine starts dumping sand at the rate 20 m^3/min, forming a pile in the shape of a cone. the height of the pile is always twice the length of the base diameter. after 5 minutes, how fast is the base radius increasing? include steps.

Base radius is increasing by 2.88 m after 5 minutes

Step-by-step explanation:

Given:-

Height of cone (h) =2 base diameter(d)

Machine starts dumping sand at the rate of 20

So,

Volume of cone in 1 min = 20

Now, Volume of cone in 5 mins = Volume of cone in 1 min

Volume of cone in 5 mins = 20

Volume of cone in 5 mins = 100 ---------(equation 1)

Now, Let base diameter of cone = b

height of the cone = h

formula for volume of cone is,

Volume of cone (V) =

----(since r=)

 ---------(equation 2)

Now substituting equation 1 in equation 2,

---------(as )

By cube rooting both the sides we get,

----------------(diameter)

 ---------------(radius of base at 5 mins)

Therefore base radius is increasing by 2.88 m after 5 minutes

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

50- 250 is correct i did that one too

step-by-step explanation: