+++++++++++ math question +++++++++++

Test Preparation SAT Preparation
1

<p>1.
A positive integer is said to be "tri-factorable" if it is the product of the three consecutive integers. How many positive integers less than 1000 are tri-factorable?</p>

<p>the answer = 9
please explain..</p>

<p>2.
....................._
...................<em>l..l
.................</em>l....l
...............<em>l......l
...............l</em>____l
( 1 square on the top, 2 squares below , 3 squares belower and 4 squares at the bottom )
The figure above shows an arrangement of 10 squares each with side of length "k" inches. The perimeter of the figure is "p" inches. The area of the figure is "a" square inches. If
"p" = "a" , What is he value of "k" ?</p>

<p>the answer = 8/5 or 1.6
please explain</p>

<p>Thank you ......</p>

2

<p>Q1: I think you can calculate this.</p>

<p>Q2:p=16k
a= 10k2 (k square)
=> a = p
Solve this quadratic equation => k=8/5</p>

3

<p>i can’t help you with 1 since i have the same question.</p>

<p>for 2,
16k= p ---- eqn 1(perimeter)
10 (k^2) = a -------eqn 2(area) </p>

<p>since p=a, sub it into eqn 2
10 (k^2) = p
from eqn 1, p=16k so sub into this
10 (k^2) = 16k
10(k^2) - 16k = 0
5 (k^2) - 8k =0
Factorise</p>

<p>k (5k-8) =0
5k-8 =0 or k=0 (NA)
k = 8/5</p>

4

<p>Q1 (1,2,3) (2,3,4) (3,4,5) (4,5,6) (5,6,7) (6,7,8) (7,8,9) (8,9,10) (9,10,11).
Beyond these 9 pairs, any coupling would give a product greater than 1000. Its very simple if u spot those 3 numbers whose product exceeds 1000.
Hope this helps.</p>

5

<p>Q1: 1.2.3=6
2.3.4=24
…
9.10.11=990
Q2: p=10k</p>

6

<p>i got the first one…ok
but any other easier explaination for the number 2… i don’t get it

  1. (k^2) what is this mean ?
  2. quadratic equation emmmm is it -b radical ± 4ac blah blah blah… ?</p>

<p>explaination for grade 6 drop out would be nice…</p>

7

<ol>
<li> A positive integer is said to be “tri-factorable” if it is the product of the three consecutive integers. How many positive integers less than 1000 are tri-factorable?</li>
</ol>

<p>(x)(x+1)(x+2)</p>

<p>This is three consecutive integers multiplied by each other. What you can do is plug this equation into your graphing calculator as y = (x)(x+1)(x+2)</p>

<p>Look at the table of values (2ND, GRAPH) and see how many values are under 1000. You’ll notice the 9th value is 990, and the 10th is 1320, so the answer is 9.</p>