OlympusHero

I suck at geo, but i'll try this anyway.

Call AD y and DC z. Then AC = sqrt(y^2+z^2). We also know that yz = GE * CE. CE, by our equation, is equal to yz/GE. Therefore, our answer should be (sqrt(y^2+z^2))/(yz/GE). I'll leave you to simplify that.

Hope this helped!

The spinner has 5 sides. Therefore (assuming the sides are all different, which the problem should've noted), there are 5 outcomes when you roll the spinner. When you flip a fair coin (notice the problem should've noted the coin was fair), there are always 2 outcomes (heads/tails). Therefore, by the Multiplication Principle, (look that up if you don't know what it is) the answer is 5 * 2  = 10

Hope this helped!

Hmmm..

Yay now I figured it out!!!!

We know that a/b = r

Then a = rb

so a + b = rb + b = b(r + 1)

a - b = rb - b = b(r - 1)

Therefore the ratio is (b(r+1))/(b(r-1))

This is just (r+1)/(r-1)

And that's the answer!!!!!

Here you go!

https://web2.0calc.com/questions/help_4754
 

Happy Birthday CPhill! I've only been here a short time, but I can already see that you are very nice and a very good answerer!

Keep helping people!

The trick to these problems, at least for me, is to find the maximum, and then count backwards and find the possible values.

Hope this helps!

This may be incorrect, but I'll give it a try.

The tallest person is in the back row, with three spots. 3 ways to place him. The shortest person stays in the front row, 3 ways to place him. Normally, our answer would just be 3*3*4! (4! means 4*3*2*1) but two friends are identical twins, so they are indistinguishable. Therefore our answer is (3*3*4!)/(2!) = 108. 

Hope this helped!

a) i^4 = 1, i^5 = i, i^6 = -1, i^7 = -i, i^8 = 1, i^9 = i, i^10 = -1.

b) The explanation is the the pattern cycles in powers of 4. Every 4th power (like i^4 or i^8) is always 1. Anything 1 above a multiple of four (ex. i^9) is always just some multiple of four multiplied by i, so it would be i. For anything two above, it would be a multiple of 4 * i^2, so -1. For i^3*multiple of 4, it would be -1. And then i^4 * multiple of 4 is 1 and we cycle again.

c) We know that i^2000 = 1, and therefore i^2001 = i^2000*i = 1*i = i.

Hope this helped!