Exponents
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- ismith0
Answers are C and B. Thanks for the help all, I just needed to see the steps everyone was going through to see where I was stopping short or going too far.
- fyoucher10
Well whadya know....
- Pupsipu0
yea if you know how to enter the problem
- mg330
they only make you learn this stuff to try and make you insane (they succeeded here) and to derive an odd sense of personal satisfaction from watching you suffer.
- Pupsipu0
it's supposed to form more neural connections in your brain, which might make you smarter in general.
but we have to answer his problem, otherwise he will be upset emotionally and do bad on the SAT and think no one really cares about him. He take this srsly.
- monNom0
432 = ((a^1/2)*(b^1/3))^6
6√432 = (2√a)*(3√b)
(6√432)/(3√b)= (2√a)
a = ((6√432)/(3√b))^2
a = (3√432)/1.5√b
a = 16.42
- neverblink0
hmm.. in that first; couldn't it be all anwsers except E ?
v = square root
18v18 = rvt
rvt = 76.367531. r & t = positive
2. r>tr*t = 18
r*t = 36
r*t = 108
r*t = 162
r*t = 324----------------
18^2 * 18 = r^2 * t
r^2 * t = 5832if r*t = 18 then
t = 18/rr^2 * 18/r = 5832
r * 18 = 5832
r = 5832/18 = 324t = 18/324 = 0.555~
324v0.555~ = 76.36753 = 18v18if r*t = 36 then
t = 36/rr^2 * 36/r = 5832
r * 36 = 5832
r = 5832/36 = 162t = 36/162 = 0.222~
162v0.222~ = 76.36753 = 18v18if r*t = 108 then
t = 108/rr^2 * 108/r = 5832
r * 108 = 5832
r = 5832/108 = 54t = 108/54 = 2
54v2 = 76.36753 = 18v18if r*t = 162 then
t = 162/rr^2 * 162/r = 5832
r * 162 = 5832
r = 5832 / 162 = 36t = 162/36 = 4.5
36v4.5 = 18v18if r*t = 324 then
t = 324/rr^2 * 324/r = 5832
r * 324 = 5832
r = 5832 / 324 = 18t = 324/18 = 18
r !> t
- hektor9110
E = mc-squared
- Infirm0
The first one can be simplified to (r^2)t=5832, for integers this gives 16 different solutions, but as both numbers are positive, this is reduced to 8, and as r>t, there are only the following options: r=54 and t=2, or r=27 and t=8, therefore C is the correct answer.
The second can be (a^3)(b^2)=432, this gives a=3 b=4, therefore B is the correct answer.
- drgss0
I think both questions are solved by factorization
In first question all answers are multiples of 18, in the form
r * t = k * 18, where k = 1,2,6,9 or 18As people have pointed out the first equation is simplified to
r * r * t = 18^3, setting in r * t = k * 18
r * k * 18 = 18^3
r * k = 18^2
k = 18^2 / r
so basically we are looking for integer divisors of 18^2 = 2*2*3*3*3*3 up to k = 18, which are
2, 3, 4, 6, 9, 12, 18 etc
we have 4 matches
k = 2 which gives r = 162 and t = around 0.5, which is not an integer
k = 6 , r = 54 and t = 2
k = 9, r = 36 and t = 4.5, not an integer
k = 18, r = 18, t = 18, which is not an option since r must be r > t
so the answer is r = 54 and t = 2And the second question
a * a * a * b * b = 432 = 2 * 2 * 2 * 2 * 3 * 3 * 3 = 3 * 3 * 3 * (2 * 2) * (2 * 2)
so a = 3 and b = 4