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<p>Well drawing a 3-D picture of the pool may help a lot on this one. Since you know on one end (10 ft deep end) is constant for 25 ft, you can easily find the volume required to fill that area:</p>
<p>10 * 50 * 25 = 12500 square feet</p>
<p>Now for the other end. You can probably solve this various ways, but here’s what I did.
First I find the volume of that entire side (disregarding the upward slope):</p>
<p>10 * 50 * 50 = 25000 square feet</p>
<p>10 because I’m disregarding the fact that it’s sloping (for the moment)
50 for the width of the pool
and 50 because 75 - 25 = 50</p>
<p>Now you need to find the area missing by finding the volume of the “ramp”. Extend the line on the bottom of the pool and draw a vertical connecting the bottom of the pool up to the existing 4 ft deep end. To find the volume of that missing area, here’s what you have to do:
(50<em>50</em>6)/2 = 7500 square feet</p>
<p>50 is width of pool
50 is the remaining length
6 is the difference between the two depths of the pool
You have to divide by 2 because the area missing isn’t a rectangular prism, but a triangular prism</p>
<p>Find the area of the right side of the pool by 25000 - 7500 = 17500 square feet</p>
<p>Add the left side of the pool: 17500 + 12500 = 30000 square feet << Therefore J is your answer</p>
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<p>If it’s a system of two linear equations WITHOUT a solution, that translates to there is no intercept. That being given, you can eliminate F, H, and K because according to the line they gave you on the graph, those equations will definitely create an intersection. (-2x means it’s sloping downwards but the given line is sloping upwards, meaning there will be an intercept; y = 2 creates a horizontal line, crossing the y-axis at 2, definitely intersecting the line) </p>
<p>What’s left is G and J. Because the given line crosses the y-axis at 3 (0,3), J cannot be the correct answer because 2x + 3 means that the line crosses the y-axis at 3, creating an intersection. The only answer remaining is G.</p>
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<p><a href=“http://img179.imageshack.us/img179/2985/act3t.jpg[/url]”>http://img179.imageshack.us/img179/2985/act3t.jpg</a></p>
<p>Geometric sequence means each sequential term is multiplied by some constant.
Because a1 (first term) = n and a2 (second term) = an, you can deduce the rate of increase to be a. </p>
<p>In other words, to move from the first term to the second term, the base equation would have looked something like n(a)^(x-1), x being the number of term it is.
So the first term was solved by n(a)^(1-1), which is the equivalent of n because a^0 will always be one. </p>
<p>That said, the 1000th term is n(a)^(1000-1) which is the same as n(a)^999. Therefore, your answer must be A. (a^999)(n)</p>
<p>I hoped this helped (and that those are the correct answers, hahahaha)</p>
