ETERNITY

Hello Guest!

By the quadratic formula, $x = \frac{-b + \sqrt{b^2 - 4c}}{2}, \frac{-b - \sqrt{b^2 - 4c}}{2}$. The difference of these is $\frac{2\sqrt{b^2 - 4c}}{2} = \sqrt{b^2 - 4c}$. Setting this equal to $|b - 2c|$, it follows that (after squaring) $b^2 - 4c = (b-2c)^2 = b^2 + 4c^2 - 4bc$. Thus$$0 = 4c^2 + 4c - 4bc = 4c(c - b + 1).$$As $c \neq 0$, it follows that $c = \boxed{b - 1}$.

Hope this helped! 

Good job, Guest!

@AboveGuest Very clever method... I didn't even think of using similar triangles!

Expanding on the solution, $\sqrt80$ can be simplified to $4\sqrt{5}$, so the number that goes in the green box is 4.

I believe the problem didn't take into account that the time zones are different, since if it did, then the problem would probably have told us which time zones to follow and what time zones the times it gave us were in.

And who downvoted the above post? This was an amazing attempt by a user, and if it was the wrong answer, at least congratulate them on trying!

Hello Guest!

You're pretty lucky. I just happened to be on :D

So, since they're both PM, we don't have to do any conversions.

We know that 7 hours have passed, and also 25 minutes from 1:20 to 8:45.

Converting the 7hours to minutes and adding 25, we get 445 minutes. Javier's flight took 445 minutes to complete.

I hope this helped! 

Oh okay... Guess I'm learning something new every day! 

What is sec though? I know it stands for secant, but I don't know what it is...

Lol geometry is one of my worst subjects.

Thanks!

Hello Cdortch.

SOLUTION:

Do you know Heron's Formula? It will greatly benefit you in this problem.

Heron's formula states that the area of a triangle is equal to the square root of the semiperimeter times... well, I'll just write it out. $s$ is semiperimeter. \[A=\sqrt{s(s-a)(s-b)(s-c).}\] Now, when we plug in the values, we find that the area of a smaller triangle is $\sqrt{\dfrac{9}{2}(\dfrac{9}{2}-1)(\dfrac{9}{2}-4){(\dfrac{9}{2}-4)}}$. We then multiply this by 2.

Putting the above equation into a calculator, we get $\frac{3\sqrt{7}}{2}$.

Hope this helped! 

Good to see you, CPhill! (You're back in the leaderboards again! )

Problem 005.

I think you really should try this one yourself before checking your work with my solution. These should be simple now that you've read my previous solutions.

This problem is just plugging values into the 1st kinematic equation, or $v_f - v_i = at$, which gives us $v_f=-29.47$

Please tell me if I got these correct!

Hope this helped! 

Problem 004:

Since air resistance is neglegible and impossible to calculate, we know that the final x velocity is equal to the initial x velocity. So the answer is the same as Problem 003, or $10.96m/s$