2^(x^2 - 3x - 2) = 2^(2*(x-4)) * 2^(3x)
2^(x^2 - 3x - 2) = 2^(5x - 8)
x^2 - 3x - 2 = 5x - 8
x^2 - 8x + 6 = 0
Using vieta's, -b/a = --8/1 = 8.
=^._.^=
Nice, but I think that it can be simplified further.
sqrt(a) - sqrt(b) = sqrt(8-4sqrt(3))
a + b - 2sqrt(ab) = 8 - 4sqrt(3)
a + b = 8
ab = 12
a = 6, b = 2. *Note that a > b because sqrt(8-4sqrt(3)) is positive.
sqrt(6) - sqrt(2) = sqrt(8-4sqrt(3))
z^7 + 8z^4 - 2iz^3 - 16i = 0
z^4(z^3 + 8) - 2i(z^3 + 8) = 0
(z^4 - 2i)(z^3 + 8) = 0
So... (z^4 - 2i) = 0 or (z^3 + 8) = 0
Remember to thank the past answerers to your questions. :))
For each ball, you have 5 different options.
First ball has 5 options, second ball has 5 options, third ball has 5 options, and fourth ball also has 5 options, 5*5*5*5 = 625.
(2a + b) - (a + b) = 1 - 2 (mod 10)
a = 9 (mod 10)
a + b = 2 (mod 10)
9 + b = 2 (mod 10)
b = 3
a = 9, b = 3, a - b = 6
She will go up if she gets more heads than tails, and she will go down if she gets more tails than heads.
If when stops at the 7th floor or higher, that means she went up.
Since there's an equal chance of getting more heads than tails and getting more tails than heads, the answer is 1/2.
3^x = y
y^2 - 6y - 27 = 0
(y-9)(y+3) = 0
y = 9, or -3.
However, y can't be negative since y = 3^x.
y = 9
3^x = 9
x = 2
The number x is in the domain when (x - 3)^2 - (x - 18)^2 is non negative.
(x - 3)^2 - (x - 18)^2 >= 0
(x^2 - 6x + 9) - (x^2 - 36x + 324) >= 0
30x - 315 >= 0
30x >= 315
x >= 10.5
The chance they both have it is .44 * .44 = .1936.
.1936*100 = 19.36%
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Nice solution, but it says raised to the 8th instead of 2nd.
To get the constant term, we need 4 "6x" and 4 "1/(3x)".
Using the binomial theorem, the coefficient is 8C4 = 70.
70 * (6x)^4 * (1/(3x))^4 = 1120
