This is how u would find horizontal and vertical asymptotes
It is given in the question that
A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by
And the edge length of the base is 12 cm, the edge length of the base is decreasing at a rate of 2 cm/min, the height of the box is 6 cm, and the height is increasing at a rate of 1 cm/min.
Here we differentiate V with respect to t, and we use product rule, that is
Substituting the given values , we will get
![[tex]dV/dt = 2(12)(6)(-2)+ 12^2(1)](https://tex.z-dn.net/?f=%5Btex%5DdV%2Fdt%20%3D%202%2812%29%286%29%28-2%29%2B%2012%5E2%281%29)
[/tex]
So at that moment, the volume is decreasing at the rate of
because the denominator is on the bottom, you have to find a number which both 12 and 9 can be divided by. In this case the only answer that isn't a decimal is 3
Let's eliminate x. To achieve this, mult. the 2nd equation by 2, obtaining
-8x + 2y = 10. Now add this result to the first equation:
8x-2y= -10
-8x + 2y = 10
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0
The two equations actually represent the same line. Without an x- or a y-value, we cannot solve for the value of the other variable. There are infinitely many solutions.
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<span>I believe this question is referring to purchasing a discount on a loan's interest rate by putting more towards closing costs. For mortgages, sometimes they will allow you to "buy" a smaller interest rate. For example:
Loan A has an interest rate of 4.5% and no closing costs.
Loan B has an interest rate of 4.375%, but has $1000 in closing costs.
Normally, Loan A would be the better choice if you plan on keeping the home short term, but Loan B would be more beneficial for keeping the loan long-term. I don't really care to spend the time that is necessary to come up with an actual scenario, but I hope that helps enough for you to understand the question</span>
