SAT Math TOUGHIES..

Test Preparation SAT Preparation
1

<p>hey everybody..
came across 2 of these questions on a SAT practice test n somehow dont know how to begin with.. any help will really b appreciated..
thanks...</p>

<p>1) A sphere with a radius of 4 is inscribed in a cube whose edge length is 8. What is distance from the centre of the sphere to a corner of the cube?</p>

<p>(A)4root3
(B)8root2
(C)8
(D)8root3
(E)root35</p>

<p>2)If a,b and c are constants, what is the maximum number of points of intersection between the graph of y=-|ax^2+bx+c| and a circle?</p>

<p>(A)2
(B)3
(C)4
(D)6
(E)8</p>

<p>thanks a lot ppl...</p>

2

<p>For question 1, you realize that it's like finding the diagonal of a box whose sides are 4. root(16+16+16) = root(16*3) = 4 root 3</p>

<p>For question 2, this graph has the most turns when it crosses the x axis.
\ /
\ /
\ ^ /
\/ \/
Sry, this is my best depiction of a parabola with the portion under the x axis reflected upwards. As you can see, the most points of intersection occurs when the circle is sitting snug in the parabola and the lil' hill, so 3 points of intersection</p>

3

<p>I think the answer for the second question should be 4. I understand how you can get 3 intersections, but if you just shift the imaginary circle down a little, there will be 4 intersections.</p>

4

<p>Oh shoot, I'm crazy! Sorry, didn't read the quesion properly, it's intersections not tangents... Ok well if you have a really slim parabola. (sufficiently slim and long that say, the vertex is say at y = -5000, and at y = 5000, x = +- 2, a pretty slim parabola). Now if you put it into the absolute value function, you'll get kinda a thin "W" shape. Then you'll be able to put a circle on it to have 8 intersection points.</p>

5

<p>Oh yeah, absolute value... you're right it would be 8 intersections.</p>

6

<p>ok people i understood ur explanations... thanks a load.. but what i dont get is how u got the graph of =-|ax^2+bx+c|. wud really appreciate help on dat... </p>

<p>thanks again..</p>

7

<p>hey... anybody there... really want some help on graph of -|ax^2+bx+c|.</p>

8

<p>Refer to [url=<a href="http://s88199767.onlinehome.us/parabola.gif%5Dimage%5B/url"&gt;http://s88199767.onlinehome.us/parabola.gif]image[/url&lt;/a&gt;]. It uses a positive parabola as an example, but the concept is the same.</p>

9

<p>syn.. amazing.. how on earth did u get that???</p>