Another SAT Math Question

Test Preparation SAT Preparation
1

<p>Official SAT Studty Guide
Test #5
Section 3
Page 357</p>

<p>"If p, r, and s are three different prime numbers greater than 2, and n = p x r x s, how many positive factors, including 1 and n, does n have?</p>

<p>I came up with 5, but that book says that the answer is 8. Please explain.</p>

<p>And my second question is:</p>

<p>"h(t) = c - (d - 4t)^2
At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h above, in which c and d are positive constants. If the ball reached its maximum heights of 106 feet at time t = 2.5, what was the heights, in feet, of the ball at time t=1?"</p>

<p>I don't even know how to start. The answer is 70. Please explain.</p>

2

<p>Never mind.. I have it now.</p>

3

<p>lets say
P:2
R:3
S:5</p>

<p>2x3x5=30
factors of 30 are
1 2 3 5 6 10 15 30; 8 factors.</p>

4

<p>anhtimmy is incorrect. The question states that the primes are bigger than 2. </p>

<p>3x5x7 = 105 .</p>

<p>Prime factorization</p>

<p>You get</p>

<p>3,5,7,15,21,35 </p>

<p>Thats 6.</p>

<ul>
<li>itself and 1 = 8.</li>
</ul>

5

<p>i m just explaining it theoretically.... the factors are 1,n,p,r,s,ps,pr,sr------total 8 factors</p>

<p>second que:
when t=0 then h(t)=6....so 6=c-d^2........ (i)
when t=2.5 then h(t)=106.....so 106=c-(d-10)^2... (ii)</p>

<p>now substract (i) from (ii) and solve for d....u will get d=10
so c=106</p>

<p>now put the values t=1,c=106,d=10 in the equation of h(t)
u will get 70 as answer</p>

6

<p>since you already have the answer to the first one I'll helpw/ the 2nd one.</p>

<p>Basically you have to set up a system of equations.</p>

<p>c - (d - 4(0))^2 =6
c - (d - 4(2.5))^2=106</p>

<p>c - (d^2) = 6
c - (d-10)^2 =106</p>

<p>c - (d^2) =6
c- (d^2) + 20d - 100 =106</p>

<p>20d - 100 = 100</p>

<p>d=10
c=106</p>

<p>106 - (10 - 4(1))^2</p>

<p>= 70</p>

7

<p>I didn't see the "greater than two part"
This is why I can't get a 800 on Math..... ugh</p>

8

<p>Thanks meadow36--- after all the explanations that I have ready on multiple sites yours was the easiest to understand.</p>

<p>I knew how to do it.. my problem was that I forgot to factor (d-10)^2 to (d-10)(d-10)
I simply just made it d^2 + 100. I don't know what I was thinking-- math is slowly escaping from my brain.</p>

9

<p>that ball problem is probably the hardest math sat question i've seen</p>