SupersonicMan12

if x^2 + 9 = 10, then x would have been +- 1, both less than 5. ELIMINATED

if 3x - 8 = 10, then x = 6, also ELIMINATED.

But i think there is a typo, do you mean "f(x) = x^2 + 9 if x > -5", then the first case would work, and the answer would hence be 0.

The pythagorean theorem tells us that the distance from P to Q is sqrt(64+9) = sqrt(73). A = pi r^2. A = 73pi.

\(\frac{\ln{b}}{\ln{a}}\)

If "the square" refers to the large one, then 50

If it's the small one, then 100.

Can you show us the steps?

@You-Know-Who, i don't think the conjugate root theorem applies here, since the coefficients are complex too.

We see that t + 8 is always the largest side.

The triangle inequality requires t+8 < t+1+t-1 to be true, which simplifies to t > 8. 

OHHHHHHH thank you! How come i didn't see!!!

a = 15/13, and b = 780, a+b = 781 2/13 or 10155/13

All real numbers.

(x-3)^2 - 1

Hi, CPhill!! I'm new to web2.0calc :) 

The problem basically asks how many numbers are relatively prime to 2019, as those that are cannot be further simplified.

Thus, Euler's Totient Function gives, (1 - 1/3)(1 - 1/673) 2019 = 1344.

@CPhill, for instance, 6/2019 gives 3/673 :)