First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.
The sum
can be written as:
,
<span>
from the binomial expansion formula: </span>
.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>
</span>
.
This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.
At x=5.4, the expression
, which is equivalent to
, takes it smallest value.
Substituting, we would find
=32.4 This is the smallest value of the expression.
For x=5.4, y=-3x+18=-3(5.4)+18=1.8.
Answer: (5.4, 1.8)
Answer:
<em>Answer: D. Jake paid his loan in 12 months</em>
Step-by-step explanation:
Jake took out an interest-free loan of $2,401.56 from the bank to buy a car.
Since he has to pay no interest for the loan, the monthly payments are totally used to cover the amount of the loan.
He paid the bank $200.13 each month, thus the total months needed to pay the loan is:
Answer: D. Jake paid his loan in 12 months
37.22 gallon or if you round up it would be 37 and 1/4
It looks like the differential equation is
Check for exactness:
As is, the DE is not exact, so let's try to find an integrating factor <em>µ(x, y)</em> such that
*is* exact. If this modified DE is exact, then
We have
Notice that if we let <em>µ(x, y)</em> = <em>µ(x)</em> be independent of <em>y</em>, then <em>∂µ/∂y</em> = 0 and we can solve for <em>µ</em> :
The modified DE,
is now exact:
So we look for a solution of the form <em>F(x, y)</em> = <em>C</em>. This solution is such that
Integrate both sides of the first condition with respect to <em>x</em> :
Differentiate both sides of this with respect to <em>y</em> :
Then the general solution to the DE is