<p>In the 2nd edition blue book the 2nd test, section 2 question 18 the one with the cylinder fitting into a box, anyone want to explain that to me in a logical basic way.
I went on the college board answers for it but it just didnt click in my mind. I am looking for a basic explanation.
Thanks CC!</p>
<p>Sure!</p>
<p>The formula for the volume of a rectangular box is (length x width x height). Now: imagine you put a box over the cylinder and it is a perfect fit.</p>
<p>(1) The height of that box will be the same height as the cylinder (in other words: h).
(2) The width of the box will have to be exactly as “wide” as the cylinder. What is the “widest” dimension of the cylinder? It is the diameter (on other words: d).<br>
(3) The length of the box will also have to accommodate the diameter of the cylinder, so it will also be “d.”</p>
<p>So then, (l x w x h) becomes (d x d x h) or in other words (d^2h).</p>
<p>AHHHH i dont get how D is the length!!!</p>
<p>Pinz, try this:</p>
<p>Draw a circle inscribed in a square. This means that the square should “just fit” around the circle, so that the square touches the circle at 4 points. Now draw a horizontal line through the center of the circle that touches the square at 2 of these points. This is the diameter of the circle. Notice that this diameter has the same length as a side of the square. Thus the area of this square is d^2, where d is the diameter of the circle.</p>
<p>Now, the base of the cylinder is exactly this picture. </p>
<p>Does that help?</p>
<p>thank you dr. steve a logical explanation to my problemm!!!
expect more questions very soon i need to get up to a 650!!!</p>
<p>practice test 3 2nd edition blue book section 2
Questions 17, 18, 20 help me CC!!!</p>
<p>Pinz, I’ve lent out my copy of the blue book at the moment, but if you write the questions or provide a link to them I’d be happy to answer them for you using the most effective SAT strategies.</p>
<p>ahhhhhh get you blue book back!!!</p>
<p>(x-8)(x-k)= x^2-5kx+m</p>
<p>In the equation above k and m are constants. If the equation is true for all values of x what is the value of m?</p>
<p>OK. This would be considered a very hard question for the SAT. I’m going to go ahead and FOIL the left hand side.</p>
<p>x^2-kx-8x+8k=x^2-5k+m</p>
<p>x^2-(k+8)x+8k=x^2-5k+m</p>
<p>The coefficients of x must be equal. Thus k+8=5k. Subtracting k from both sides gives 8=4k. So k=2</p>
<p>The constant terms must also be equal. So m=8k=8*2=16.</p>
<p>So m=16.</p>
<p>Let me know if you need me to clarify any steps.</p>
<p>By the way, I assume this is a grid in question. If it’s multiple choice, you should also give the answer choices. I often have quicker ways to get the solution if there are answer choices.</p>
<p>Method 2: Choosing values for x.</p>
<p>Since the equation is true for all x, we can substitute in any values of x we like and get a true equation.</p>
<p>x=0 8k = m
x=8 0 = 64-40k+m = 64-5(8k)+m = 64-5m+m = 64-4m</p>
<p>So 64-4m = 0. Thus 4m = 64, and m = 16.</p>