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
I think it is 56, is this a multiple choice question?
There are 21 red pens. For every 3 red pens, there is 1 blue pen.
Let's make these into a fraction equation.
21/p=3/1
p is the number of blue pens we have yet to find.
First, cross multiply.
21x1=21
px3=3p
Now, we have an equation of
21÷3p
We set it equal to 1, and we solve it.
21÷3p = 1
(21÷3p)×3p=1×3p
21=3p
21÷3=(3p)÷3
7=p
So, if there are 21 red pens, there are 7 blue pens.
We add these together to find the total number of pens the teacher has.
21+7=28
The teacher has 28 pens total.
Answer:
Step-by-step explanation:
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Good evening ,
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Here we used A and B properties
Look at the photo below for the explanation,
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:)
