<p>1) If rs^2t^3u^3 > 0 and u < 0, which of the following must be true?
(a) rt < 0
(b) urt< 0
(c) r > 0
(d) t > 0
(e) st > 0</p>
<p>The answer is A</p>
<p>2) To arrive on time, a ship needs 5 hours to complete a voyage. If the ship must arrive in 4 hours, by what percent must the speed of the ship be increased?
(a) 15%
(b) 20%
(c) 25%
(d) 27%
(e) 30%</p>
<p>The answer is C</p>
<p>3) The figure above shows a rectangular solid with width x, length y, and height z. If xy=20, yz=10, and zx=18, what is the volume of the rectangular solid?
(a) 60
(b) 70
(c) 80
(d) 90
(e) 100</p>
<p>The answer is A</p>
<p>4) In the figure above, PQ is the arc of a circle with center O. If the length of arc PQ is 4, what is the area of sector OPQ? (The figure is half a circle and angel POQ is 45)
(a) 54 pi
(b) 48 / pi
(c) 32 pi
(d) 32 / pi
(e) 16 pi</p>
<p>The answer is D</p>
<p>I just need the explanation and how to get the answer</p>
<h2>1) wasn’t written clearly enough. do you mean r * s^(18tu) or (rs)^(18tu)?</h2>
<p>2) rt = d
Let d = 100 for the sake of simplicity (we can set d = to whatever we want since it’s the ship is always travelling the same distance in the problem).</p>
<p>r*5 = 100
5r = 100
r = 20 <<usual rate of the ship</p>
<p>r*4 = 100
4r=100
r = 25 <<rate of ship if it wants to make it in 4 hrs</p>
<p>Percent change = |new - original|/original</p>
<h2>(25-20)/20 = .25 = 25%</h2>
<p>3) Best thing to do here is to plug in numbers.
xy * yz * zx = x^2 * y^2 * z^2</p>
<p>x^2 * y^2 * z^2 = 3600
sqrt(3600) = xyz</p>
<h2>xyz = 60</h2>
<p>4) Sector OPQ = 1/8 of circle O (based on 45 degree angle)
Find the radius:
(1/8)(2pi<em>r) = 4
2pi</em>r = 32
pi<em>r = 16
r = 16/pi
pi</em>r^2 = area
pi*(16/pi)^2 = 256/pi
(256/pi)/8 = 32/pi</p>
<p>1) u^3 is negative. We need the whole thing to be positive.
r * s^2 * t^3 must be negative in order to “neutralize” u^3 and make the whole thing positive. Since s^2 is positive, r<em>t^3 must be the negative part. Since t^3 and t have the same sign, r</em>t must also be negative.</p>
<p>Thus rt > 0.</p>
<p>s^2 is always positive, so (r)(t^3)(u^3) must be positive. Rewrite as (r)(t^2)(t)(u^2)(u), and since t^2 is always positive, and u^2 is always positive, (rtu) must be positive. We’re told that u is negative, so for rtu to be positive, rt must be negative.</p>
<p>You can do this more quickly by rewriting the original expression as (s^2)(t^2)(u^2)(rt)(u), and then applying the logic above.</p>
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