Can someone help me solve these math problems?

Test Preparation SAT Preparation
1

<p>1.
[x=|0|1|2]
[y=|10|a|b]
The value of x and y in the table above are related so that (y-1) is directly proportional to (x+1). What is the value of b+a?
The answer is 9.</p>

<p>2.
Point A and B are on the surface of a sphere that has a volume of 36*pie cubic feet. What is greatest possible lenght, in feet, of line segment AB? (The volume of a sphere with radius r is V=4/3(pie)r^3.
answer is 6.</p>

<p>3.
The graphs of the equations y=x^2 and y=k-x^2, where k is constant, are shown above. If the lenght of AB(line) is an integer, which of the following cannot be the value of K?
a)2
b)8
c)12
d)18
e)32
the answer is C</p>

2

<ol>
<li><p>im getting 47 lol…</p></li>
<li><p>its the diameter of the sphere</p></li>
<li><p>wheres the graph???</p></li>
</ol>

3

<p>1 is interesting and I’d love for someone to explain that</p>

<p>2) A and B are on the surface of a sphere and so the greatest length they can be is the length of the diameter. Use the equation of volume and the volume of the cube to help you find the diameter through r (Radius)</p>

<p>36pi=(4/3)pi*r^3 <----you can cancel out pi since it’s on both sides
Do algebra and it turns out that r=3
The radius is 3 so the diameter is just twice that, 6, so the greatest distance between the two points is 6.</p>

<p>Yeah the picture of the graph would help… to see where they intersect… etc…</p>

4

<ol>
<li>I calculated this and my answer is 47 a= 19 and b= 28</li>
</ol>

<p>The answer you provided is a difference of the two 28-19= 9. I suppose the answer is erroneous or you meant what is a-b</p>

<ol>
<li><p>The longest line would be the diameter so u would have transpose to get this value</p></li>
<li><p>I cant solve w/out a pic. A pic is needed.</p></li>
</ol>

5

<p>what i attempted to do for number 1 was this.</p>

<p>direct proportionality: y = kx</p>

<p>y-1 = k (x+1)</p>

<p>plug in the givens.</p>

<p>10-1 = k (0+1)</p>

<p>9 = k</p>

<p>make a general equation.</p>

<p>y-1 = k(x+1)</p>

<p>y = kx + k + 1</p>

<p>y = 9x + 9 + 1</p>

<p>y = 9x + 10</p>

<p>plug in to solve for a and b.</p>

<p>a = 9(1) + 10</p>

<p>a = 19</p>

<p>b = 9(2) + 10</p>

<p>b = 28</p>

<p>a + b = 47</p>

<p>however, what’s interesting is that the OP might have made a mistake in transcribing the problem. the problem may have asked for a-b, which is 28-19 = 9 indeed.</p>

<p>other than that, i’m just completely wrong.</p>

6

<p>y - 1 = k(x + 1) is the equation of proportionality. Let’s solve for k using values of x and y.</p>

<p>10 - 1 = k(0 + 1)
k = 9</p>

<p>y - 1 = 9(x + 1) is then our final equation which we can use to find a and b and hence a + b.</p>

<p>a - 1 = 9(1 + 1)
a - 1 = 18
a = 19</p>

<p>b - 1 = 9(2 + 1)
b - 1 = 27
b = 28</p>

<p>I think you wanted b - a, which would be 28-19 = 9.</p>

<ol>
<li>Using V = 4/3 pi r^3 to get the radius of the sphere.</li>
</ol>

<p>4/3 pi r^3 = 36 pi
4/3 r^3 = 36
r^3 = 27
r = 3</p>

<p>The largest segment containing two points on a sphere is the diameter, 2r, or 2*3 = 6.</p>

<ol>
<li>I don’t know what AB is, but this might be helpful.</li>
</ol>

<p>The intersection between the two graphs is found by
x^2 = k - x^2
2x^2 = k
x^2 = k/2</p>

<p>k/2 must be a perfect square in order for AB to be an integer. All the choices work except 12 (which gives 6, not a perfect square).</p>

7

<p>ohhh for number 2 i read the question wrong. I found r which is 3.05 and though that the question asked for the greatest distance “on” the sphere. I didnt think it was a line, damn i really need to read the questions carefully. </p>

<p>The graph is a parabola aiming up (this one is y=x^2), and another parabola aiming down (this one is y=k-x^2.)</p>

8

<p>niceeeeeeee</p>

<p>did u write #1 wrong?</p>

9

<p>@ i took the sat, No you’re right. Thank You. Thanks to jamesford for number 3.</p>

10

<p>Yeah my friend took the may sat and got the answers. I took the test and got 3 wrong, so i wanted to know how to solve them, just in case I find them again in the october sat.</p>