proyaop

To give a little hint, the formula of interest rate to get the money you have is: \(A = P(1 + {r\over n})^{nt}\) where:

A = Amount you have after a certain period of time.

P = Original amount, principal amount.

r = Annual interest rate.

n = Number of times the interest compounds each year.

t = time in years.

Hope that helps and gives you a little lift on how to get started with this problem :)

I think applying the formula is the smartest way to do it, I did it a little unorthodoxly, thank you Guest! 

The answer would be D.

The reason so can be determined by taking a look at each option.

Option A would get us \(x^4 = m^2\), and wouldn't help us in anyway.

Option B would get us \({x^2\over m}=1\), and would only get us what the value of \(x^2\over m\), but that isn't what we are looking for.

Option C would get us \({x^2\over2}={m\over2}\), and would get us nowhere.

Option D would get us \(x = \sqrt{m}\), and get us the value of \(x\) in terms of \(m\), which is more helpful, and since \(x\) is normally the unknown or what we are trying to solve,

Option D is the best way to solve the equation \(x^2 = m\).

Actually \(({4\over3})^3\) is \(4^3\over3^3\), that simplifies to \(64\over27\).

Thus the correct answer to this problem is \(64/27\). 

The 5th term is 20. The pattern is the n-th term is 3(n-1) + 8, so the 100-th term of the pattern is 3(99) + 8 or 305. Thus, all the numbers added from 20 to 305 would be added together, with a difference of 3 between each number. Since we know there are a total of 96 numbers added together, we can subtract 17 from each number, then divide each number by 3. Then the numbers from 1 - 96 would be added together, which equals 4656.

Then we multiply 4656 by 3 to get 13968. Then since we subtracted 17 from 96 numbers, we have to add (17 x 96) to 13968. That gets 15600. Thus, the answer is 15600.

Correct me if I got it wrong :D

Thanks anyway:

I got 452 :)

It was 5 :(

thanks asinus and thx for the reminder melody :D

Thanks for double checking, also I think you can use AC as the diameter of a circle, then knowing ABC is a right triangle and then using the pythagorean theorem, thanks anyway :D

The original expression is:

\(\sqrt{2} + \sqrt{3} + {1\over2\sqrt{2} + 3\sqrt{3}}\)

Next we can simplify the fraction part of the expression by multiplying the denominator by the difference of squares;

The expression is now:

\(\sqrt{2}+\sqrt{3} + {3\sqrt{3}-2\sqrt{2}\over19}\)

Then we can multiply the first two terms of the expression by \(19\) to get:

\({19\sqrt{2}\over19} + {19\sqrt{3}\over19} + {3\sqrt{3}-2\sqrt{2}\over19}\)

Then adding up the numerators and simplifying we get:

\(17\sqrt{2} + 22\sqrt{3}\over19\)

Thus, \(a\), \(b\), and \(c\) are \(17\), \(22\), and \(19\) respectively. 

Since we are looking for the sum of our three "variables", we add \(17+22+19\) to get:

\(58\), which is the answer.

:D

I got \(\sqrt{39}\) with long equations and polynomials, can someone double check thanks!