CPhill

Call the radius of the circle, r.

The area of the surrounding square, ABCD = 4r^2

The area of the square inscribed in the circle = 2r^2

The area of the circle = pi*r^2

So.....the shaded area = the area of the circle - the area of the inscribed square =  [pi*r^2 -2r^2]

So....the probability  that  a point is chosen in the shaded area  = 

shaded area  / total area bounded by ABCD =

[pi *r^2 - 2r^2] / [4r^2]  =

r^2 [ pi - 2]/ {r^2 *4]  =   [  r^2  cancels ]

[pi - 2 ] / 4        (E)

3^x = 12       take the log of both sides

log 3^x  = log 12       and we can write

x * log 3   = log 12      divide both sides by log 3

x =   log 12  / log 3  =  about  2.262

If the growth rate doubled every week, it would grow by 100% per week.

Since the growth rate triples every week, it grows by 200% per week.

This is easy to see.....

If 1 person is sick at the start.......by the end of the first week, 2 more would be sick. And 2 is 200% of 1. So, 3 people are sick at the end of the first week- triple that of the start.

At the end of the second week,  6 more would be sick , and 6 is 200% of 3. So, 9 people total are sick at the end of the second week - triple that of the beginning of the second week.......etc.

2sqrt(5)   =   5sqrt(2)      ????

Note that....if we squared both things, and they were equal to begin with, they should still be equal....so we have

4 * 5   = 25 * 2      ????

20  =   50    ????  ....  nope.....       thus.........2sqrt(5)   <  2sqrt(2)........!!!!!

F = 75 + 5m     ......   m in this case  = 50- 30   = 20........so we have

F = 75 + 5(20)  =  75 + 100   = $175

Notice the pattern:  [you may have to shrink your screen to see the complete results]

A string  of 20 1's   = 10000001000000* 1,111,111 +  111,111  

A string of 40 1s = 1000000100000010000001000000100000 * 1,111,111 +  11,111  

A string of 60 1's =

100000010000001000000100000010000001000000100000010000 * 1111111 + 1111  

80 1's    10 groups of 1000000 append 1000 * 1,111,111  +  111   

100 1's =    13 groups of 1000000 append100 * 1,111,111 + 11  

So, 100 1's   divided by 1,111,111  =

1000000100000010000001000000100000010000001000000100000010000001000000100000010000001000000100 +11/1,111,111

So....the remainder is 11

Maybe Heureka knows an easier method to calculate this.....????

-2, -8, -32, -96, -384

I don't like the grapher in this calculator.......I use Desmos......easy to use and it will handle exponential functions........here's the website address  :  https://www.desmos.com/calculator

(3c)4 =    3⁴  * c⁴  =    81 c⁴

A parabolic graph has a vertex  (h , k).......but.......this is a square  root graph......

It is the shift of the parent graph (the square root of x]  to the left 2 units

There is no vertical shift of this graph compared to the parent graph

Also......this graph is stretched vertically by a factor of 3 compared to the parent graph

Here is a graph of both functions...........https://www.desmos.com/calculator/txwoettdln