7(x+2)
Let's find the common term in this expression to factor it out. it is 7.
Factoring is the opposite of distributing.
If we distribute, we will get the original expression.
Next:
45-27k
Here, the common term is 9:
9(5-3k)
12ab+7b - the common term is b:
b(12a+7)
y^2-9y.
Here the common term is y:
y(y-9)
8r-32r² the common term here is 8r:
8r(1-4r)
16gh+28gh: the Common Term is 4gh:
4gh(4+7)
21w²-77wx The common term is 7w:
7w(3w-11x)
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Answer:
The draining time when only the big drain is opened is 2.303 hours.
The draining time when only the small drain is opened is 5.303 hours.
Step-by-step explanation:
From Physics, we know that volume flow rate (), measured in liters per hour, is directly proportional to draining time (
), measured in hours. That is:
(Eq. 1)
Where is the proportionality constant, measured in liters.
From statement, we have the following three expressions:
(i) <em>Large and small drains are opened</em>
(Eq. 2)
(ii) <em>Only the small drain is opened</em>
(Eq. 3)
(iii) <em>Only the big drain is opened</em>
(Eq. 4)
By applying (Eqs. 3, 4) in (Eq. 2) and making some algebraic handling, we find that:
(Eq. 5)
Whose roots are determined by the Quadratic Formula:
and
Only the first roots offers a solution that is physically reasonable. Hence, the draining time when only the big drain is opened is 2.303 hours. And the time needed for the small drain is calculated by the following formula:
The draining time when only the small drain is opened is 5.303 hours.
