<h1>1 is z=0. The question asked which would give a point equidistant from (0,0,5) and (0,0,-5). They are both five units away from z=0. Even if the point is (10,6,0), they are still the same amount of units away.</h1>
<h1>2 - It’s two, three, or four zeros. See earlier in the thread for explanation. Basically, g(x) and f(x) can either never intersect (in which case there are four zeros), intersect at one zero (in which case there are three zeros), and intersect at both zeroes (in which case there are two zeros).</h1>
<p>Consider each of the following scenarios:
f(x) = (x-4)<em>(x-2) and g(x) = (x-3) * (x-1). Zeros at x=1, 2, 3, and 4
f(x) = (x-4)</em>(x-2) and g(x) = (x-4)<em>(x-1). Zeros at x=1, 2, and 4
f(x) = (x-4)</em>(x-2) and g(x) = 4<em>(x-4)</em>(x-1). Zeros at x=2 and x=4</p>
<h1>3 - You misunderstood the question. If you have a cone and cut a section off from the bottom of it, you get a new cone with a smaller height and a smaller radius. The original numbers were 18 inch height and 12 in radius. Since r = 2h/3, you can plug that in to V=1/3<em>pi</em>r^2<em>h and get V = 4/27</em>pi*h^3. With an 18 in height, V = 2714. Since the volume decreased by half, the new volume was 1357. Work backwards to find the new height and you get 14.</h1>
<p>@CoolKidBro
4-D? What are you talking about?</p>
<p>x=y=0 would be line encompassing all z values; how would every point on that line be the same distance from (0,0,5) and (0,0,-5)?
It is clearly z=0; i.e. the xy plane… Test the distance for any (x,y,0) point from the two given points…it’s always the same. zach12 is right…</p>
<p>I’m also not sure what you are talking about on 2 and 3…</p>
<p>@CoolKidBro: Sorry mate, but your limit is stupidity. You clearly don’t know what the zero of a function is… it’s when y=0, not when x=0. Look at this example.</p>
<p>usually the cutoff is 44 out of 50 is an 800</p>
<p>For the cone one, I’m pretty sure the height is half of the original height, because the volume of a cone is V=pi<em>r^2</em>h/3</p>
<p>If the volume is cut in half by cutting it in half across the middle, then the radius stays the same. As a result, in order to counter the new volume that is one half the original, the height needs to be cut in half</p>
<p>This was the way I approached the question, and coming out of the test I was pretty sure its the right answer. Anyone have an explanation that says differently? Because now I’m not too sure</p>
<p>If I got this one wrong I’m screwed because that would mean I got a 43 or lower, which is sub-800</p>
<p>Err… how does the radius stay the same?
Imagine looking at it from a side, like a triangle, with the radius as the base.
Now cut the triangle parallel to the base in half.
The height AND radius change.</p>
<p>It’s a similar figure in three dimensions, so since the vol is 1/2 the original, Each dimension is 1/2^(1/3) of the original. Thus the height is 18*1/2^1/3=14.29</p>
<p>Sorry to go off topic, but for the one with two stamp machines, one at 25 units/hr and 20 units/hr, was it 27 hrs (A)? As in, use time as “x”, set 25 X + 20 X = ____ (whatever the total # of stamps were) and then divide to get X? </p>
<p>hardworking- yes to the first one, and I think yes to the 2nd. I don’t really remember the choices xD
self-indulgent- there was a 15 and a 13.5, along with something like an 11</p>
Oh well.</p>