A very large tank initially contains 100L of pure water. Starting at time t=0 a solution with a salt concentration of 0.5kg/L is added at a rate of 6L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 4L/min. Answer the following questions. 1. Let y(t) be the amount of salt (in kilograms) in the tank after t minutes. What differential equation does y satisfy? Use the variable y for y(t).
Answer (in kilograms per minute): dy/dt= ?
2. How much salt is in the tank after 30 minutes
Answer (in kilograms):?

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

step-by-step explanation: s

question says to graph a triangle (xyz) and reflect it over the line y=x to create triangle x'y'z'.

we know that line y=x has both coordinates equal like (1,1), (5,5) etc so we can easily graph that reflecting line.

description of transformation:

we can see that x and y coordinate gets switched after transformation like (2,8) changed to (8,2)

what do you notice about the two line segments you drew:

we see that line segments xp and x'p are of same length and perpendicular to the reflecting line y=x.

do you think you would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line? :

yes, i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line.

how do you know? :

by measuring the length of yk and y'k.