Quick Math Help from Bluebook

<p>If any of you could be so kind to go to page 585, #16 (Bluebook) and explain how to get the answer for me. I would just type it up myself, but it's got a diagram and whatnot. I tend to get this type of problem (find the area of the shaded region type question), but this one is tripping me up! Thanks so much!</p>

<p>The area of the whole thing is 2 since each line segment is 1. 2 x 1 = 1</p>

<p>The area of each quarter circle is (pi * r^2)4. R is 1, so the area is pi/4.</p>

<p>The total area is rectangle - (2*quarter circle) which is 2 - pi/2</p>

<p>Ah, thanks. I see.</p>

<p>What about #19? I tried plugging in numbers and it doesn't get me what I want.</p>

<p>If a, b, c. and f are four nonzero numbers, then all of the following proportions are equivalent EXCEPT</p>

<p>a) a/f = b/c THE ANSWER
b) f/c = b/a
c) c/a = f/b
d) a/c = b/f
e) af/bc = 1/1</p>

<p>It is A.</p>

<p>They want to see which of those 5 equations does not equal the other 4.</p>

<p>By multiplying the 2nd equation by (c/b) you get the 3rd one.
By inverting the 3rd you get the 4th.
By multiplying the 4th by (f/b) you get the 5th.</p>

<p>Or you could just choose a set of numbers that works with 4 of the equations but not the last one. a=2 b=3 c=4 f=6</p>

<p>Thanks for the help!</p>

<p>Wait, so dividing across =/= equivalent? Cool.</p>

<p>Is that right tho? Im too lazy to make my own proof</p>

<p>Your a little confused...
Do you mean to divide across to convert the first equation to the second?</p>

<p>The first equation would become c/f = b/a, not f/c = b/a.</p>

<p>Of course dividing across is equivalent. But bad math is definitely not equivalent.</p>