Atank initially contains 40 ounces of salt mixed in 100 gallons of water. a solution containing 4 oz of salt per gallon is then pumped into the tank at a rate of 5 gal/min. the stirred mixture flows out of the tank at the same rate. how much salt is in the tank after 20 minutes ?

The amount of salt that is in the tank after 20 minutes is;

A(20) = 267.56 Oz

Initial amount of salt in tank; A(0) = 40 Ounces

A solution containing 4 oz salt per gallon is pumped into the tank at a rate of 5 gal/min.

This means rate in oz/min = 4/1 × 5/1 = 20 oz/min

A'(t) = 20 - [(A(t)/(100)) × 5/1]

A'(t) = 20 - A(t)/20

Rearranging gives;

A'(t) + A(t)/20 = 20

Multiplying through by the integrating factor gives;

A'(t) + (A(t)/20) = 20

A(t) = 400  + C

Divide through by to get;

A(t) = 400 + C

At initial condition of A(0) = 40, we have;

40 = 400 + C

C = -360

Thus; at time (t), the amount of salt left is given by;

A(t) = 400 - 360

A(20) = 400 - 360

A(20) = 400 - 132.44

A(20) = 267.56 Oz

Read more at; link

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.