5x - 9y = -13 -2x + 3y = 4
1 answer:
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Let us assume last year the price of the item = $x.
After increase in price by 15% the new price = x + 15% of x = x+ 0.15x = 1.15x.
There is a 25% discount for employee.
25% of 1.15x = 0.25 × 1.15x = 0.2875 x.
Price after discount = 1.15x - 0.2875 x = 0.8625x.
The employee pays $172.50.
Therefore,
0.8625x = 172.50.
Dividing both sides by 0.08625.
Answer:
It will take about 35.49 hours for the water to leak out of the barrel.
Step-by-step explanation:
Let be the depth of water in the barrel at time
, where
is measured in inches and
in hours.
We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that
where is a constant of proportionality.
Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:
Multiply by
Multiply by
Take integral
Integrate
Isolate
We know that the water level starts at 36, this means . We use this information to find the value of
.
At t = 1, y = 34
So our formula for the depth of water in the barrel is
To find the time, , at which all the water leaks out of the barrel, we solve the equation
Thus, it will take about 35.49 hours for the water to leak out of the barrel.