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 Hi Ron,

I just doubled checked; your cat’s name is available for use on this forum, and so is Ron [catname].

The moronic post above is consistent with the themes of with our forum’s new Village Idiot –the syntax is a little different from his style. Our village idiot usually signs his name–even when posting as a guest. So maybe it’s his brother, Crooked.   

I doubt anyone with a functional brain (who knows you) would think you wrote that. ...Your style is more Gracie Allen. 

LoooooooooooL

I mucked around quite a lot with the second one before I got it.  (Maybe there are some shortcut techniques)

anyway:

It should help you a lot if you work out the value of        \((1-\sqrt3i)^3\)

I will look at the send one a little later.   

That is not quite right.  it is (-4i)^50 = (-4)^50 * i^50 = 4^50 * i^50

You need to work out what i^50

once again you do it with a pattern

hint:

i^1=

i^2=

i^3=

i^4=

i^5=

what is the pattern?

i^ 50 = ?

How many lattice points does the line y = -2x + 28 pass through?

Hello Guest!

The line y = - 2x + 28 goes through 15 grid points.

  !

What real value of produces the smallest value of the quadratic t^2 - 9t - 36 + 3t^2 - t + 10?

Hello Guest!

\( t^2 - 9t - 36 + 3t^2 - t + 10\\ f(t)=4t^2-10t-26\\ f'(t)=8t-10=0\\ 8t=10\\ \color{blue}t= \dfrac{5}{4}\)

The value \(t = \dfrac{5}{4}\) produces the smallest value of the term \(t^2 - 9t - 36 + 3t^2 - t + 10.\)

  !

3 = -4 * g(0)

g(0) = - 3/4

[EDA] = 1/6[ABC]

How do you know 

Hint:    angle CAD = tan^-1(ME / AM)

okay so the answer is 4^{50}, I understood the first one.

for the second one, I cannot divide 35 by 2 or is it what I should do?

\((-\sqrt2+i\sqrt2)^{100}=((-\sqrt2+i\sqrt2)^{2})^{50}\\~\\ (-\sqrt2+i\sqrt2)^{2}=2-2-4i = -4i \)

yep but opening braces goes like this:

\((2-4*i+2)^{50}\)

I have no idea how to proceed from here and I don't know if I opened the braces correctly

i have just looked at the first one.

Hint:

\((-\sqrt2+i\sqrt2)^{100}=((-\sqrt2+i\sqrt2)^{2})^{50}\)

Nice work Solviet.

Divide everything by  -24

then complete the squares to get    (x-h)^2 + (y-k)^2 >= r^2

So I came till here, but don't know how to continue:

\(|x+yi+4+3i|\leq|5\cdot(x+yi)+10-9i|\\ |(x+4)+i\cdot(y+3)|\leq|(5x+10)+i\cdot(5y-9)|\\ \sqrt{(x+4)^2+(y+3)^2}\leq\sqrt{(5x+10)^2+(5y-9)^2}\\ x^2+8x+16+y^2+6y+9\leq25x^2+100x+100+25y^2-90y+81\\ x^2+8x+y^2+6y+25\leq25x^2+100x+25y^2-90y+181\\ -24x^2-24y^2-92x+96y\leq156\)

Hi Solveit  

I let   z=x+yi

and this is the graph I got.

I don;t intend to do all the working but I will say that

\(|z+4+3i|\\ =|(x+4)+(y+3)i|\\ =(x+4)^2+(y+3)^2\\ etc\)

see if you can do it from there,     

From 1 000 000 000     to  9 999 999 999    is   9 000 000 000    ten digit numbers

    only the ones that end in a zero are divisible by 10

       that is 1/10 of the total

          900, 000,000

3==F + 3D, 

23==F + 8D, solve for F, D

Use substitution to get:

F== - 9 - this is the first term

D== 4 - this is the common difference.

Your sequence looks like this:

-9 , -5 , -1 , 3 , 7 , 11 , 15 , 19 , 23 , 27 , >>Number of terms = 10>>Total Sum == 90

The number of ways is 100*98*96 = 940800.