Thank you. :))
=^._.^=
This has a really nice method.
B will be left of A 50% of the time, right of A 50% of the time.
5*4*3*2*1 total ways to be in a line, 50% of which are where B is on the left of A.
5*4*3*2*1/2 = 60
a = 1/4 (first term)
r = 1/2 (ratio)
n = number of terms
15/32 = 1/4((1/2)^n - 1)/(1/2 - 1)
Try to solve it by yourself from here. :))
15/8 = ((1/2)^n - 1)/(-1/2)
-15/16 = (1/2)^n - 1
1/16 = (1/2)^n
n = 4
Sine(x) returns a number from -1 to 1, not an angle.
I think it's -1, 9, -18.
Another cool trick you can use to find the sum of coefficients is to just plug in c as 1.
-(3-1)(1+2(3-1))
This works because the final answer in expanded form will look like xc^2 + yc + z, and if c = 1, x1^2 + y1 + z = x + y + z, which is the sum of the coefficients. :))
I don't know what this "cis" function is.
So I would love if someone could please explain to be.
On Youtube, there is a video by Harold Walden proving that cis(a)*cis(b) = cis(a+b).
(sqrt(2)/6 * sqrt(6)/4) * (cis(3pi/5) * cis(2pi/3))
sqrt(12)/24 * cis(3pi/5 + 2pi/3)
sqrt(3)/12 * cis(19pi/15)
x^2 - 16x + 3 = 0
Try plugging in these numbers to the quadratic formula and find the 2 numbers.
Then, subtract them. :))
Nice work, but I think it's multiples of 4 instead of just 4. :))
You're welcome. :))
As for the first one, try using mod 7.
5, 25, 125, 625
5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1...
So it repeats every 6.
Can you take it from here?
2.) A palindrome is a number that reads the same forward and backward. The largest possible 4-digit palindrome in base 3 can be expressed as a 3-digit palindrome in another base b>2. What is b?
The largest 4 digit palindrome in base 3 is 2222.
Trying all the bases, in base 6, 2222 (base 3) = 212 (base 6).
