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

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116

answer: x=1

step-by-step explanation:

f(x) = g(x)

x - 2 = -1

x = 1

therefore the graph should be a line showing x=1 which is vertical and passes on 1

hope it !