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I recently noticed that CPhil got removed from top users... is he ok?    

When I click the "down arrow" at the bottom of the list, CPhill's name reappears at the top.    

_.

See image below....

Area of the triangle on the right is   1/2 b h ===  1/2 (8 tan 45)(8)  

    there are TWO of these triangles that make  the larger isosceles right triangle .

       So the total area is       2   *   (1/2)(8 tan 45)(8)   units²         <=========== You can finish

I can see from my diagram that MB=AM   but the reason eludes me....

How did you determine this?

You are right guest, CM is definitely not a diameter. I apologize for my error.

CM is NOT diameter!!!

CM would be the diameter only if AC = BC!!! But this is not the case.

Hint:     arc AM = arc BM

P = pi + √8 

Distance from 0,0 to 15,9   is the radius     =   sqrt (15^2 + 9^2) = sqrt306

x^2 + y^2 = 306   is your circle

Let the no of cards, he buy on each day = x

--> So total no. of cards in 10 days

                 = 208 + 10x

Given in 5 days, he had bought 5/23 at the total

no. of cards he was given and had bought

in the 10 days, end becomes

        5x = 5/23 ( 208 + 10x)

         23x = 208 + 10x

          23x - 10x = 207

            13x = 208

               x = 16

5 * 16 = 80 cards

(10-4i)(4-5i)+(-15+20i) =

40 - 50i -16i + 20i^2 - 15 + 20i    collect like terms   ( note that i^2 = -1     so + 20 i^2 = -20)

5 -46i

(5^x) = 100    square both sides

(5^x)²  == 5^2x  = 100² = 10 000

(94+89+88+92+85+ x) / 6 = 90      Just solve for 'x'

To add a bit, the reason 12^n can't be wholly divisable by 20 is because 20 = 2^2 * 5 and 12 = 2^2 * 3. 

That means that 12^n will only have factors of 2 and 3 (assuming n is an integer). 

Therefore, it will never be able to divide out the 5 in 20. 

=^._.^=

If you know f(0), f(1) = f(0) + 2(1) + 1

Continue this process until you get to 4. :))

=^._.^=

Thank you jugoslav!! That's also what I got :))! And thanks to Guest, now I understand some of "Locus"

The equation for the locus.

I think this would be it.

\((x-2)*(x-5+i)*(x-5-i)\\ =(x-2)((x-5)^2+1)\\ =(x-2)(x^2-10x+26)\\ etc \)

Find the largest integer n for which 12^n evenly divides 20.

Hello Guest!

\( n\in \mathbb Z\\ z=\dfrac{12^n}{20}\\\)

\(\large z\notin \mathbb Z\)  

\(12 ^ n\) is in no case wholly divisible by 20.

  !

deleted as in error.

Write your question in English and more people may be able or prepared to help you.

A sector of 144 degrees is removed from a circle of radius 15, and the remaining portion is folded into a cone. What is the angle at the vertex of the cone?

The original radius will become the slant height, so the slant height will be 15units

360-144=216 degrees

\(New\; Circumference=\frac{216}{360}*2\pi r\\ New\; Circumference=\frac{216}{360}*2\pi *15\\ New \;Circumference\approx18\pi\;\;units\)

Now find the cone radius

\(C=2\pi r\\ 18\pi=2\pi r\\ r=9\;\;units\)

Now draw the pic and use trigonometry to find any angle that you please. 

they're different variables and I cant figure out how to apply them so still please help

How many sugared buns were there in the bag at first?

Hello Guest!

\(\dfrac{x+1}{2}+\dfrac{1}{2}(x-\dfrac{x+1}{2})+7=x\\ 0.5x+0.5+0.5x-0.25x-0.25+7-x=0\\ -0.25x=-7.25\)

\(x=29\)

29 sugared buns were there in the bag at first.

(15 at David, 7 at Peter, 7 at Andrew)

  !

3x^2-24x+72

3 ( x^2 -8x)     + 72

3 (x-4)^2         + 72 -48

3 (x-4)^2 + 24          <====== you can finish

Perimeter = pi√8

https://web2.0calc.com/questions/in-the-diagram-below-angle-pqr-angle-prq-angle-str