<ol>
<li>If the center of the circle x (square) + y(square) + ax + by + 2 = 0 is point (4,-8) then a+b =?
Answer: 8 </li>
<li>The vertical distance between min and max values of function y = |-(square root of 2) * sin(square root of 3x)|
Answer: 1.414. For this question, anybody has an alternative solution other than using graphing calculator?</li>
<li>If f(x) = 3x(square) + 4x + 5, what must the value of k equal so that the graph f(x-k) will be symmetric to y-axis
Answer: 2/3</li>
<li>|2x - 1| = 4x + 5 has how many numbers in its solution set
Answer: 1. When I solved this question by solving 2 equations 2x-1 = 4x+5 and 2x-1 = -4x-5, I got 2 values of x, but when graphing out, the 2 functions |2x - 1| and 4x+5 only intersects at one point, meaning they have one value of x. Anybody knows why?
Thanks in advance</li>
</ol>
<ol>
<li><p>Complete the square to get (x + a/2)^2 + (y + b/2)^2 = r^2 for some r (we don’t actually care what r is). The center of this circle is at (-a/2, -b/2) = (4, -8), so a = -8 and b = 16, and a+b = 8.</p></li>
<li><p>sin(sqrt(3x)) can vary between -1 and 1 (including the endpoints). The minimum value of |-sqrt(2)*sin(sqrt(3x))| is 0 (when sin(sqrt(3x)) = 0), and the maximum value is sqrt(2) (when sin(sqrt(3x)) = +/- 1). Their difference is sqrt(2).</p></li>
<li><p>Complete the square to get f(x) = 3(x + 2/3)^2 + c for a constant c. Then f(x - 2/3) = 3x^2 + c which is symmetric about the y-axis, so k = 2/3.</p></li>
<li><p>Your two equations are incorrect. |2x-1| = 2x-1 or -2x+1, checking each one gives</p></li>
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<p>2x-1 >= 0 --> 2x-1 = 4x+5 <–> x = -3
2x-1 < 0 --> -2x+1 = 4x+5 <–> x = -2/3</p>
<p>However x = -3 is not a solution since 2x-1 is not >= 0 if x = -3. Therefore x = -2/3 is the only solution.</p>
<p>thanks, but what do you mean by “complete the square”? for question 1 and 3.</p>
<p>See <a href=“Completing the square - Wikipedia”>http://en.wikipedia.org/wiki/Completing_the_square</a></p>
<p>Thank you</p>
<p>@MITer94 I have a few other questions!
1, In how many distinguishable ways can the 7 letters in “MINIMUM” be arranged if all letters are used each time?
Answer: 420.
2. The statistics below provid the summary of IQ scores of 100 children
Mean: 100
Median: 102
Standard deviation: 10
First Quartile: 84
Third Quartile: 110
About 50 of the children in this sample have IQ that are?
Answer: between 84 and 110</p>
<ol>
<li><p>7!/(3!*2!) = 420 (7! ways to arrange the letters, divide by 3! to account for three M’s and 2! to account for two I’s). These kinds of counting questions come up pretty frequently, so I recommend that you practice counting problems a bit so that you can solve them correctly every time.</p></li>
<li><p>The first and third quartiles are roughly where the 25%ile and 75%ile data points are, so about 50% of the data are between these quartiles.</p></li>
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