Melody

its 1.3 repeater seconds

I think it is possible that you have mistyped the question but what you HAVE asked is still quite doable.

Subtract the second from the first and you get

  \(6ab^2=6\\ 3ab^2=3 \)

So now I have  

\(a^3+3=679\qquad and \qquad a^3-3=673\\ a^3=676\\ and\\ 3*\sqrt[3]{676}*b^2= 3\\ \sqrt[3]{676}*b^2= 1\\ b=\pm \sqrt{1-\sqrt[3]{676}}\\ a-b= \sqrt[3]{676} \pm \sqrt{1-\sqrt[3]{676}}\\\)

You need to check that, I could easily have made a careless mistake.

NOW check your question, i really do not think you wrote it down properly.

I got the same answer as EP.

Hi OldTimer

\((a+\sqrt b)(c+\sqrt d)\\ =ac+bd+a\sqrt d + c\sqrt b\\ \text{This will only be rational if, and only if, the last two terms cancel each other out ie}\\ a\sqrt d = -c\sqrt b\\ \text{which simplifies to}\\ \frac{c}{a}=-\frac{\sqrt d}{\sqrt b} \)

24.6    that is an answer.   (maybe not to this question though)

Nice try Mmm but you forgot some of the posibilities   

The Boomtown Bears are playing against the Tipton Toros in a baseball tournament. The winner of the tournament is the first team that wins three games. The Bears have a probability of 1/5 of winning each game. Find the probability that the Bears win the tournament.

I will assume that it is imposible to draw.

P(B wins) = 1/5

P(B wines 3 games out of 3) =    1/   5^3                                                      =  25 / 5^5

P(B wins 3 games out of 4) =  4C3 * (1/5)^3 * (4/5) = 4 * 4 / 5^4 = 16 / 5^4  =  80 / 5^5

P ( B wins 3 games out of 5)  =  5C3 * (1/5)^3 *( 4/5)^2 = 10 *  16 /  5^5      =   160 / 5^5

add them together    25+80+160 = 265

265 /  5^5  simplifies to   53/625  =  0.0848

So the prob that the bears win is  8.48%

\(y=2(3^x)\qquad and \qquad y=6(2^x)\\ so\\ 2(3^x)=6(2^x)\\ \frac{3^x}{2^x}=3\\ 1.5^x=3\\ log1.5^x=log3\\ xlog1.5=log3\\ x=\frac{log3}{log1.5}\\ x\approx 2.7095\)

You can take if from here.

Let the 3 pieces by   x,     6 - y   and  y-x     long

Note that when you add these up you get 6

You know that each of these must be between 0 and 6 units long.

GRAPH the sample space.  Find Area of sample space

Now overlay that with the desired area where all the pieces  are less than 3 units long.  Find the area of this event

Probability = area of event/ area of sample space

This is called probability contour mapping.