Suppose that a large mixing tank initially holds 900 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 4 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).)

dA/dt= 12-2A(t)/900+t

Step by step Explanation:

Given:

rate of 3 gal/min

concentration of the solution entering is 4 lb/gal,

The equation of the solution can be expressed as

dA/dt = R(1)- R(2)

Where R(1)=( concentration of the salt at inflow* rate of input of given brine)

R(2)= ( concentration of the salt at inflow* rate of output of given brine)

R(1)= 3 gal/min× 4 lb/gal=12Ib/min

But the solution is been pumped slowly, the rate of the accumulation can calculated as;

(3 gal/min- 2 gal/min)=1gal/min

But after t min we will be having 900+t gallons present in the tank

CHECK THE ATTACHMENT FOR COMPLETE EXPLANATION

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

a) 0

step-by-step explanation:

i^413 x i^0 = 0 as any number multiplied by a zero is

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