Melody

Try proofreading your question.

I expect you can work out (or count)  part a  just as well as any of us can.  

There are 9 individual digits then 2 digits for each number from 10 to 99.     How many is that?

Part b.  Count how many zeros there are and put that number of the total number of digits.

Part c.  Do the other 2 parts then look for patters that you can add together.

You got it :)

Hi Juriemagic,

\(\displaystyle 3y=1+x+x^2 \qquad \qquad \sum_{k=3}^4 x(k-2)^2=5y\)

Second one

\(x(3-2)^2+x(4-2)^2=5y\\ x+4x=5y\\ 5x=5y\\ x=y\)

Sub this into the first one ansd solve.

If you have problems let us know.  :)

the meaning of your question is not clear.

If I understand the question correctly

10C5  *  0.7^5 * 0.3^5 = approx 10.29 %

It is easiest if it is of the form

\(f(x)=Acos[b(x-p)]+M\)

A is the amplitude (if neg then it is upside down)

2pi/b  is the period

y=M is the midline

p is the phase schift

Now I think of it in bits, sketch it as you go. So that you build up the graph step by step

consider

\(1) y=cos(x)\\ 2) y=-cos(x)\\ 3) \text{make the numbers on the x axis fit with a period of } 2\pi/b\\ 4) \text{drop or raise the graph so the centre line is }y=M\\ \\5) \text{Change the amplitude by making the bottom of the wave M-A and the top M+A }\\ 6) \text{Shift the phase by p units to the right}\), 

f(x)=-4cos(2/3x+pi/3)-3 

 it seems to be common pracice to accept that the first line is the 0 line, so it is easiest just to ignore that one

the sequence is    2,4,8,16,32

I can just see that this is   2^n    but if that is not immediately obvious to you, you can inspect it as a sequence.

since  4/2 = 8/4 = 16/8 = 32/16 = 2

this is a GP   

the first term is 2 and the common difference is 2

\(T_n=ar^{(n-1)}\\~\\ T_n=2*2^{(n-1)}\\~\\ T_n=2^{(n-1+1)}\\~\\ T_n=2^n\)

The sum of the 0 row is 2^0 = 1

the sume of the nth row is  2^n

the sum of the 10th row is 2^10  = 1024

the sum of the 20th row is  2^20

etc

Here is the pic, the answer is an approximation, you shouod be expected to work out the exact value.

I started with the 2 orange circles then rotate them about X by 360/12 = 30 degrees

You can see that point A is halfway between C and C'

Find the length of AX using cosine rule and then double it for  AB