Saphia1123

Ohhhh OK OK thank you so much!! This really helped :)

OHHHHH I think I just figured it out.  Would it be like A(x+y)?  So then it would be x+3y?

Thank you so much Alan!  I made a slight miscalculation when I tried multiplying by the conjugate.

How could I find the possible values of z in exponential form?  For |z|^n=1, could I just say:

the exponential form for |z|^n = 1 is e^{\frac{2\pi i}{n}} for n^{th} roots of unity.

Idk how to approach finding the exponential form for z+1

So if I have z^n = (z + 1)^n = 1, and spilt it into two equations: z^n = 1 and (z+1)^n = 1, and take their magnitudes, is that enough to say |z|=|z+1|=1 because it must be a root of unity? 

Here's a hint: what if you tried to glue two equilateral triangles together?

The expressions inside the radicals remind us of the Law of Cosines. For example, $\sqrt{a^2 - ab +b^2}$ can be interpreted as the length of the third side of a triangle in which two sides have lengths $a$ and $b$, and the angle between these two sides is $60^\circ$.

From these two glues triangles, what can we say about when equality occurs? When does A+B=C in a "triangle"?

I'm sorry.  Yes, I will not do this again in the future. Oh ok nvm I got it. :)

So this should be an equilateral triangle since two angles are 60 degrees.  This means BD + CD = BC = AB =DC.  The sin(60) is sqrt(3)/2.  So if AD=24, then each side of the equilateral triangle is 16sqrt(3).  Doing the triangle area formula of (BH)/2, we get 192 sqrt(3).  

I got this answer instead using the law of cosine: \[AB^2=25-12\sqrt{3}, AC^2= 20-8\sqrt{3},\] and \[BC^2= 7\]

Ohhhhh I see. I'm so used to seeing radians with $\pi$ I totally forgot. Thank you!  Also, the -9 works for C because it's going the opposite direction of -155,7 degrees (r=-4).  Thank you so much again

The equation to find the volume of a cone is (pi r^2 h)/3. 

The radius is half the diameter, so r=6

Now, we set the equation up by setting 340 = (pi * (6^2) h)/3

Some calculations and you get about 9 meters for the height

RAC = 27 PS my drawing is not to scale

First, combine like terms

26x>26

Then divide both sides by 26

x>1