<p>Direct and inverse variation are intuitive, right…?</p>
<p>So does that mean that in an inverse relationship, the x increases and the y decreases, and in a direct relationship, the x decreases and the y increases??</p>
<p>No, it does not!</p>
<p>In a direct relationship:
If x increases, y increases and vice versa.</p>
<p>In an indirect relationship:
If x increases, then y decreases or if y increases, then x decreases.</p>
<p>Look at these formulas and plug in numbers to see that it is true:</p>
<p>direct proportion: y = kx -> y/x is constant</p>
<p>indirect proportion: y = k/x -> y*x is constant</p>
<p>These questions are from the Dr. John Chungs SAT Math Book, but I don’t really understand his explanation to these question.
All of these questions are from Test 1 section 3.</p>
<h1>16 - (Cant draw the figure) 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?</h1>
<p>A. 60
B.70
C.80
D.90
E.100</p>
<p>I understand why he multiplied (20)(10)(18) which equals 3600. But then he square root the 3600 to give him A. 60
So my question is why did he square root the 3600?</p>
<p>NEXT QUESTION:</p>
<h1>18- There are two different means, the arithmetic, A= a+b/2 and the harmonic H= 2ab/a+b. If the arithmetic mean is equal to the harmonic mean, which of the following must be true?</h1>
<p>A. a= 0 and b= 0
B. ab= 0
C. a= 1 and b= 1
D. a= b
E. a + b=0</p>
<p>So, my question is the reasoning behind the answer being D because for C. a does not only have to equal 1 and neither does b because if you put a and b as 5 the arithmetic mean and the harmonic mean will be equal which debunks answer choice C? Is my reasoning right?</p>
<h1>19 - In the figure above, PQ is the arc of a circle with center O. If the arc PQ is 4, what is the area of sector OPQ? (BTW, in the figure in angle POQ angle O is 45 degrees.)</h1>
<p>A. 54pi
B. 48/pi
C. 32pi
D. 32/pi
E. 16pi</p>
<p>Is there a formula or somethiing…and I have no clue how to go about doing this question</p>
<p>This is all I have for right now…and thanks in advance!</p>
<h1>16: Volume is lwh (or in this case: xyz). If you multiply (20)(10)(18), you are really multiplying (xy)(yz)(zx). That is the same as: (xyz)(xyz). So, you need the square root of that.</h1>
<h1>18: your reasoning shows why C is wrong. But it doesn’t show why D is right.</h1>
<h1>18 - Well I plugged in and saw that A, B, E, were wrong, so I was left with C and D, so with C wrong that leaves me with answer choice D. And just to check I plug in D, and it works in the equations. Am i right? is that how you think I should be doing it… or is there a more effective way of doing this?</h1>
<h1>19: there is a formula. I’ll give you two related ones:</h1>
<h1>degrees in sector / # degrees in circle = length of arc / circumference of circle</h1>
<p>and:</p>
<h1>degrees in sector / # degrees in circle = area of sector / area of circle</h1>
<p>In your question, you can use the first equation to find the circumference of the circle. This allows you to find the radius, which will then tell you the area of the circle. Then you can use the second equation to solve for the area of the sector.</p>
<p>Or, you can use the S=θr formula, where S is the length of the arc, θ is the angle measure in radians, and r is the radius. In this case, the formula allows you to find the radius, which allows you to find the area of the circle, which you can then divide by 8 to get the answer.</p>
<p>For #18, I would have set the two quantities equal to each other and solved. I’ll do it stepwise:</p>
<p>a+b / 2 = 2ab / a+b
(a+b) (a+b) = 4ab
a^2 + 2ab + b^2 = 4ab
a^2 - 2ab + b^2 = 0
(a-b) (a-b) = 0
(a-b) = 0 (a-b) = 0
a = b a = b</p>
<p>So, for # 19, would I do 45/180= 4/x which would give me x=16…telling me that the circumference of the circle is 16. Thus, the radius is 4. but when I find the diameter that means it is 16… but I dont think that the diameter and the circumference can be equal… am I dong something wrong here?</p>
<p>For # 18 - You said: a^2 + 2ab + b^2 = 4ab
a^2 - 2ab + b^2 = 0
(a-b) (a-b) = 0
(a-b) = 0 (a-b) = 0
a = b a = b
But where we have a^2 + 2ab + b^2 = 4ab and when we subtract 2ab, it would give us 2ab…oh wait…
did u subtract 4ab and then got -2ab which is what you wrote on the second line… and then you factored it to give you (a-b)(a-b) =0??? If so…then I understand how you got it.</p>
<p>Go back to your first equation on #19: there are 360 degrees in a circle! So, the circumference is 32.</p>
<p>Then (using π for pi): c = 2πr. So, 32 = 2πr. So, 16 = πr. So, r = 16 / π.</p>
<p>Now you can find the area of the circle: A = πr^2. So, A = π (16/π)^2. This ends up so that A = 256 / π.</p>
<p>Finally, you can find the area of the sector, by using the other formula. I end up with 32/π. I hope that’s the right answer!</p>
<p>@ post #8: yes.</p>
<p>@ post #9 - But the figure shown is a semicircle, and not a full one, so is it still 360 degrees?</p>
<p>You did not include a diagram in your original post, and you said</p>
<p>
</p>
<p>also, have you personally ever seen a question on the SAT where you have ever had to do something like this…including using these formulas?</p>
<p>Well, I couldn’t really draw the diagram, and also in the question it says :“PQ is the arc of a circle with center O.”</p>
<p>If i was to explain the figure I would say that its the top half of a circle, and angle POQ is on the right side and angle O in POQ is 45 degrees. They placed angle O in the middle but at the half of the circle… do you see it now… or would you like me to describe it some more?
btw, thanks for your helping me… I really appreciate it</p>
<p>19) Here’s sort of a different way of solving number 19</p>
<p>Angle POQ is 1/8th of a circle (45/360)
4 is the circumference of sector OPQ</p>
<p>The formula for the circumference of a circle is 2piR. Just plug in the information.
1/8 * 2 * pi * r = 4 (We multiply by 1/8 because we are only finding sector OPQ which is 1/8, not the entire circle)</p>
<p>Now just solve the equation in terms of r
2 * pi * r = 32 (divide by 2 pi)</p>
<p>R = 16 / pi We have the radius now.</p>
<p>Now just use the area formula and remember to multiply by 1/8
1/8 * pi * 16/pi ^2 = 32/ pi</p>
<p>I haven’t personally seen one on an SAT, but in the Blue Book, Test #4, Section #3 there is one. Question #19 reads: In the figure above, QR is the arc of a circle with center P. If the length of arc QR is 6pi, what is the area of sector PQR? [The diagram looks like a piece of pie, with a central angle of 30 degrees.]</p>
<p>That question was written by the SAT people, and probably appeared on a test prior to March 2005.</p>
<p>And, it doesn’t really matter whether they draw the entire circle or not. Just use the formulas I gave you for a complete circle. It works!</p>
<p>Ok, I usually refrain from posting these types of threads, but I am planning of buying this book. I seriously, need a answer for this question.</p>
<p>Can anyone honestly tell me if this book helped you, or is helping you? I am planning on buying this book and I really want to score a 800 on the Math section. </p>
<ul>
<li>Is this book hard? (I want it hard, no homo)</li>
<li>Did this book help you?</li>
<li>Does this book have good explanations and strategies?</li>
</ul>
<p>Thank you. Please help.</p>