Please help with these BB math practice problems

Test Preparation SAT Preparation
1

<p>I have the 2nd edition, the following problems have the page numbers next to them.</p>

<p>p.337, #5
if 10,000 microns = 1 centimeter and 100,000,000 angstrom units = 1 centimeter, how many angstrom units equal 1 micron?</p>

<p>The answer is 10,000 but I don't get why.</p>

<p>p.361, #8
Sqaure root of x^2 - t^2 = 2t - x
If x and t are positive numbers that satisfy the equation above, what is the value of x/t?</p>

<p>The answer is 1.25 but I also don't get why.</p>

<p>Help is greatly appreciated.</p>

2

<p>10,000 micron = 100,000,000 angs
1 Mic = 100,000,000 angs/ 10,000</p>

<p>Square both sides, and work it out.</p>

3

<p>5) If 10,000 microns = 1 centimeter and 100,000,000 angstrom units = 1 centimeter, how many angstrom units equal 1 micron?</p>

<p>Dimensional analysis is your best friend</p>

<p>1 micron (1 centimeter/10,000 microns)(100,000,000 angstroms/1 centimeter)
All units cancel out except angstroms and you get 10,000</p>

<p>8) sqrt(x^2 - t^2) = 2t - x
If x and t are positive numbers that satisfy the equation above, what is the value of x/t?</p>

<p>sqrt(x^2 - t^2) = 2t - x
x^2 - t^2 = (2t - x)^2
x^2 - t^2 = 4t^2 - 4xt + x^2

  • t^2 = 4t^2 - 4xt
    -5t^2 = - 4xt
    -5t = -4x
    -5 = -4x/t
    5/4 = x/t
    x/t = 1.25</p>
4

<p>@ jamesford</p>

<p>no need to use dimensional analysis… just apply the transitive property.</p>

5

<p>Ah I didn’t even notice that.</p>

<p>However, dimensional analysis is basically foolproof for any type of problem with variables and several different units of measurement.</p>

6

<p>This is true. But in this case, writing everything out might have wasted you precious seconds. Always strive to find the best answer ;)</p>

7

<p>W/e, I make up for lost time by bubbling quickly :P</p>

8

<p>I always finish the math sections in like half the time… it’s sad, really.</p>