Water is leaking out of an inverted conical tank at a rate of 10700 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 8 meters and the diameter at the top is 3 meters. If the water level is rising at a rate of 26 centimeters per minute when the height of the water is 2.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Solution :

The diameter of the tank = 3 m = 300 cm

Radius of the tank = 1.5 m = 150 cm

Height of the tank = 8 m = 800 cm

The rate of increase of height of water level = 26 cm/min

∴

The water is leaking at a rate of  =  10700 cubic centimeters per min

∴ rate out = 10,700

At time 't', the height of water level is 'h' with radius 'r' and volume 'V'.

By the property of similarity of triangles we can write

Volume of water at time 't' is given as

Now differentiating w.r.t 't'

The rate of increase in tank =  rate of inward flow - rate of outward flow

 = rate of inward flow  - 10,700

rate of inflow = 10,700 +

Substituting the values we get

rate of inflow = 10,700 +

∴ rate of inward flow =

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25