There are 67 numbers that work.
a - b = 4*sqrt(5).
Together, they can eat 33/4 bowls.
Currently, I'm working on 3D Prisms. Oh, and, I'm sorry I took so long to respond to you, I didn't check this post until just now.
Honestly, you're lucky to get complete solutions at all. We're doing your work for free, and more demands aren't exactly sufficient incentives for proffering full solutions.
Because \((i, i^2, i^3, i^4) = (i, -1, -i, 1)\), we have \(i + i^2 + i^3 \cdots + i^{258} + i^{259} = 64(i - 1 - i + 1) + i^{257} + i^{258} + i^{259}\). So, the desired sum is \(i^{257} + i^{258} + i^{259} = i - 1 - i = \boxed{-1}\).
If \(z = a + bi\), then \(\overline{z} = a - bi\). So, \(z \overline{z} = (a + bi)(a-bi) = a^2 + b^2\). Since \((a, b) = (3, 5)\), we have \(z \overline{z} = 3^{2} + 5^{2} = 41.\)
You published the same question twice. Both times, you failed to provide a diagram. As such, it is impossible for any of us to help you with your problem.
Hint: the number of ways to distribute \(n\) indistinguishable balls into \(k\) distinguishable boxes is found with the binomial coefficient \(\binom{n + k - 1}{n}\).
https://web2.0calc.com/questions/sequence_123
See https://web2.0calc.com/questions/help_5568
DR = 11/8.
Could you give us a lift into what maths your expected to use ?
There are several methods that could be used.
What are you currently working on ?
Vectors, 3D co-ordinate geometry, what ?
-1*1/(1+1) = -0.5
The answer for (b) is 8, because 8 choose 0,1,2 are 1,8, and 28
Would you mind explaining how you got that answer?
So is it 72 or 90?
Edit: It's 72. Thank you for the help.