<p>If you have any SAT math problems that you're stuck with, I'd be happy to solve them and type the solution up here. </p>
<p>Anything from blue book, QAS, PR, or whatever is accepted. I need practice and what better way to do so than by helping others?</p>
<p>From the blue book:</p>
<p>Page 522 #17
Page 549 #9
Page 551 #16
Page 657 #18
Page 674 #19-20</p>
<p>I've needed help with these for a while.
Thanks!!!!!</p>
<p>Page 522, #17: </p>
<p>You are given: </p>
<p>4x + y = k
Rearrange this into
y = k-4x </p>
<p>You know that the line l is perpendicular to this, so its slope is 1/4 </p>
<p>y = 1/4x + b (b=0 since it passes through the origin) -> y = 1/4x </p>
<p>They intersect at (t, t+1), so that means the functions are equal at that point: </p>
<p>t+1 = k-4t </p>
<p>t+1 = 1/4t <---- use this equation </p>
<p>t = 4t + 4
0 = 3t + 4
3t = -4
t = -4/3 -> <a href="A">b</a>**</p>
<p>Page 549, #9 </p>
<p>Realize that since (3, -7) and (-2, -7) is one end of the diameter, the distance between that point and the center is going to be the radius, which happens to be 5. Now since the endpoint given is to the left of the center, the other endpoint must be to the right, so we add the length of the radius to the center to get (8, -7) -> <a href="E">b</a> **</p>
<p>Page 551, #16</p>
<p>Inspect the diagram to get the relationship: </p>
<p>2L = 3W </p>
<p>W = 2/3L </p>
<p>So you can now find the area, in terms of L, of an L by W rectangle:
(L*2/3L) = 2/3L^2 </p>
<p>Now since the area of the total region is 12L * 10L = 120 L^2, you divide 120L^2 by (2/3)L^2 to yield 180 -> <a href="E">b</a> **</p>
<p>Page 657, #18 </p>
<p>h(t) = c - (d-4t)^2 </p>
<p>Plug in what you are given:</p>
<p>At first, you're given at t = 0, h = 6</p>
<p>6 = c - d^2 </p>
<p>Then you have h = 106, when t = 2.5</p>
<p>106 = c - (d-10)^2 -> c - <a href="expand">d^2 -20d + 100 </a> </p>
<p>Realize you can write both in terms of c to solve for d</p>
<p>c = 6 + d^2 </p>
<p>c = 106 + d^2 -20d + 100 </p>
<p>106 + d^2 - 20d + 100 = 6 + d^2 </p>
<p>206 + d^2 - 20d = 6 + d^2 </p>
<p>206 - 20d = 6 </p>
<p>-20d = -200
d = 10 </p>
<p>Go back to the original equation: </p>
<p>c - d^2 = 6 </p>
<p>c - 100 = 6
c = 106 </p>
<p>Then, now, plug alll this junk back into the original equation: </p>
<p>h(1) = 106 - (10-4)^
h(1) = 106 - 36 = ** 70 **. </p>
<p>Page 674, #19: </p>
<p>Realize that you can take the reciprocal of the first one to yield x^(4/3) = k^(2)
then raise both to the (3/4) to get x = k^3/2 </p>
<p>Follow the same process with y to get y = n ^ 3/2</p>
<p>(xy) = (nk)^3/2</p>
<p>[(nk)^3/2]^-2/3 = (nk)^'1 = 1/nk -> <a href="A">b</a> ** </p>
<p>Page 674, #20 </p>
<p>Look at the graph: realize that h causes a shift left over by 3 units (-1 = 2 -3), and also realize that k shifts the graph down, so it's negative and moves it down by 2 units, so k= -2, h = -3 </p>
<p>so hk = 6 -> <a href="E">b</a> ** </p>
<p>WHEW!</p>
<p>thankss soo much.</p>
<p>I understand everything now.</p>
<p>For page 549, I need help with #9, but you wrote the explanation for #8. Would you please explain #9?</p>
<p>Oh, sorry: </p>
<p>Page 549, #9 </p>
<p>Plug the bounds (30 and 50) into each inequality. Whichever one yields a false statement for both is the correct answer. <a href="D">b</a> **</p>
<p>Blue book:
page 412: #17 & #18</p>
<p>For all numbers x, let the function f be defined by the f(x)=2x-3. If f(k)=5. What is the value of k?
Answer: 4
<em>confused about where to plugin what</em></p>
<p>In the xy-plane, a point with coordinates (a,b) lies on both of the lines y=2x+3 and y=1-3x.
Which of the following equations must be true?
Answer: a=4-2b
<em>the hell do i do here lmao</em></p>
<p>In triangle PQR, PQ=QR=13. If the length of the altitude drawn from Q, perpendicular to side PR is 12, what is the perimeter of triangle PQR?
Answer: 36
<em>confused about some triangle properties.. the answer isnt 13x2+12..</em></p>
<p>Thanks a lot man!</p>
<p>No doubt that the hardest questions on the SAT involve functions .. and thei graphs.</p>
<p>^More like the easiest.</p>
<p>Page 412, #17 </p>
<p>In order to "intersect", the x and y coords of line l and the function given must be equal at the intersection points. </p>
<p>0 = p^2 - 4
5 = t^2 - 4
p^2 = 4
t^2 = 9 </p>
<p>p is equal to either 2 or -2
t is equal to either 3 or -3 </p>
<p>The greatest slope is the value where y0-y1/x0-x1 is the greatest. You know the x coordinates are 0 and 5, so you want the values that make: </p>
<h2>y0-y1/(5-0) the greatest. So you have y/5. You want to maximize this value by finding the difference in the y's found that's greatest. The max is found by taking 3 and subtracing -2 from it to yield 5. The maximum slope, then, is 5/5 = ** 1 ** </h2>
<p>Page 412, #18 </p>
<p>This is a classic question. </p>
<p>First, we know rate = distance/time, so set up two equations, one representing the forward trip and one representing the back trip: </p>
<p>r1 = d/t1</p>
<p>r2 = d/t2</p>
<p>You know that t1+t2 = 1, so rewrite t2 in terms of t1: t2 = 1-t1, and plug back into the equations:</p>
<p>r1 = d/t1
r2 = d/(1-t1)</p>
<p>Notice how "d" is constant? this is what we're going to try to solve for. They say that the first rate is 45 mph and the second rate is 30 mph, so plug into the equations above:</p>
<p>30 = d/t1
45 = d/(1-t1) </p>
<p>Solve both for d: </p>
<p>30(t1) = d
45(1-t1) = d </p>
<p>Notice how both equations equal d? This means we can set them equal and solve: </p>
<p>30(t1) = 45-(45)(t1) </p>
<p>75(t1) = 45
(t1) = 45/75</p>
<p>Now that we have t1, plug back into either equation to solve for d (I'll use the first)</p>
<p>30 = d/(45/75) </p>
<p>d = ** 18** .</p>
<p>great, that makes a lot of sense. thanks so much!</p>
<p>
[QUOTE]
For all numbers x, let the function f be defined by the f(x)=2x-3. If f(k)=5. What is the value of k?
Answer: 4
<em>confused about where to plugin what</em></p>
<p>In the xy-plane, a point with coordinates (a,b) lies on both of the lines y=2x+3 and y=1-3x.
Which of the following equations must be true?
Answer: a=4-2b
<em>the hell do i do here lmao</em></p>
<p>In triangle PQR, PQ=QR=13. If the length of the altitude drawn from Q, perpendicular to side PR is 12, what is the perimeter of triangle PQR?
Answer: 36
<em>confused about some triangle properties.. the answer isnt 13x2+12..</em></p>
<p>Thanks a lot man! </p>
<p>
[/QUOTE]
</p>
<ol>
<li><p>f(x) = 2x-3
f(k) = 5
k is substituted for x, 5 is substituted for f(x). Solve for k. </p></li>
<li><p>Plug in a and b into both equations:
y=2x+3 and y=1-3x -> b = 2a + 3; b = 1-3a </p></li>
</ol>
<p>Add the equations together to yield:
2b = 4 - a; tinker with the equation to rearrange it into an answer choice. </p>
<ol>
<li>
[QUOTE]
In triangle PQR, PQ=QR=13. If the length of the altitude drawn from Q, perpendicular to side PR is 12, what is the perimeter of triangle PQR?
[/QUOTE]
</li>
</ol>
<p>See picture: </p>
<p>Keep the questions rolling! This is quite fun :)</p>
<p>May I join? or is this exclusively Arachnotrons help desk?</p>
<p>Absolutely! The more the merrier! As long as people get helped, that's all that matters.</p>
<p>Thanks a lot! :D</p>
<p>A four digit integer, WXYZ, in which W,X,Y and Z each represent a different digit, is formed according to the following rules.
1. X = W + Y + Z
W = Y + 1
Z = W -5
What is the four-digit integer?
Answer: 5940</p>
<p>If the average(arithmetic mean) of t and (t+2) is x and if the average of t and (t-2) is y, what is the average of x and y?
Answer: t</p>
<p>(as I go through more practice tests, I'll probably have lots more questions :P)</p>
<p>Sorry, but about the second question that you answered before. "In the xy-plane, a point with coordinates (a,b) lies on both of the lines y=2x+3 and y=1-3x. Which of the following equations must be true?" How did you know to add the equations together? Usually my first instinct is to use substitution which clearly didn't work.
Thanks</p>
<p>blue book pg 684 number 15.collegeboard one.</p>
<p>also this problem. There is a cube with a volume of 8. What is the distance from the center of the cube to a vertex? how is this solved?</p>
<p>the_pakalypse:
i'm sure arachnotron can explain your problems more mathematically than i can, but i can explain them to you my way:</p>
<p>for A four digit integer, WXYZ, in which W,X,Y and Z each represent a different digit, is formed according to the following rules.
1. X = W + Y + Z
W = Y + 1
Z = W -5
What is the four-digit integer?
Answer: 5940</p>
<p>if you play around with the equations, you can see that z+5=w, and when you plug in z+5 as w in w=y+1, you see that z+5=y+1, or z+4=y. then, you can plug z+5 in as w and z+4 in as y in the first equation, which gives you 3z+9=x. so, in order for 3z+9 to equal a single-digit integer (which is has to, because x is a digit in the number), z must be zero. when you plug in z=0 for your other equations, you get w=5, y=4, and x=9, giving you 5940.</p>
<p>for If the average(arithmetic mean) of t and (t+2) is x and if the average of t and (t-2) is y, what is the average of x and y?
Answer: t</p>
<p>intuitively, if youre taking the average of a number and two more than it, and then a number and two less than it, the average is going to be that number, both if you take the average of all four numbers, or if you take the two individual averages and average those together. but, if you have trouble seeing that:
just plug in values (its a great strategy!), so say t=3. then the average of 3 and 5 (aka t+2)=x, so x=4. then the average of 3 and 1 (aka t-2) is 2, which is y. then, the average of 4 and 2 is 3, which is t.</p>
<p>and for your other question, i did it by graphing it on my calculator and finding the intersection (let me know if you don't know how to do that, i'd be happy to teach you)...which is (-0.4, 2.2). when you plug those numbers into a=4-2b (or x=4-2y), it works.</p>
<p>however, i'm also interested in how arachnotron knew to add them together, because his way sounds better!</p>
