It goes in evenly 2 times
Answer:
2
Step-by-step explanation:
6x2=12 12/6=2
Answer:
x = 1 y = 2
Step-by-step explanation:
x + 3y = 7
- Subtract x from both sides.
3y = -x + 7
- Divide both sides by 3 to isolate the variable.
y = -1/3x + 7/3
- Plug the value of y into the other equation.
3x + 4(-1/3x + 7/3) = 11
3x - 4/3x + 28/3 = 11
- Add like terms.
5/3x + 28/3 = 11
5/3x = 5/3
x = 1
- Plug the value of x into the equation.
x + 3y = 7
(1) + 3y = 7
3y = 6
y = 2
Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
y'(t) = k√(y(t)) . . . . for some proportionality constant k
y(0) = 30
y(1) = 29
We observe that a function of the form
y(t) = a(t - b)²
will have a derivative that is proportional to y:
y'(t) = 2a(t -b)
We can find the constants "a" and "b" from the given boundary conditions.
At t=0
30 = a(0 -b)²
a = 30/b²
At t=1
29 = a(1 - b)² . . . . . . . . . substitute for t
29 = 30(1 - b)²/b² . . . . . substitute for a
29/30 = (1/b -1)² . . . . . . divide by 30
1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
b = 30 +√870 . . . . . . . . simplify
The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds
