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You will need to use a numerical method, such as Newton-Raphson (This graph should help with an initial guess):

Take out center tile then  80 tiles form four diagonal halves

   so diagonal is   41 tiles      

     and each side is 41 tiles

       total tiles = 41 x 41 = 1681 tiles all together     subtract the 81 yellow tiles    leaves 1600 grey tiles

We  can manipulate the Law of Cosines  to  find  the  measure  of angle KLM

[7.1^2   -8.9^2  -8.8^2 ]  / [ -2 * 8.9 * 8.8]   =  cos  KLM

arccos   ( [7.1^2   -8.9^2  -8.8^2 ]  / [ -2 * 8.9 * 8.8] )  = KLM   ≈  47.29°

So  NKL  =  47.29  * 3/5    = 28.374°

So   angle KNL  = 180  -  47.29  - 28.374   = 104.336°

And  using  the Law of Sines

LN / sin NKL = KL /sin KNL

LN  / sin ( 28.374)  =  8.9 / sin ( 104.336)

LN  =   8.9 *sin (28.374)  / sin (104.336)  ≈  4.365

Answered at  https://web2.0calc.com/questions/cphil-i-need-help

I don't see how it can equal 4 in all instances.  Substitute 1 for x and you get 1. 

I'm pretty sure there's a better way to do this. I've seen this question before. I have just forgotten how to approach it. Maybe let q(n)=p(2^n)-1/(2^n) for 0 <= n <=6 and then q(n)=n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)? Something like that? I could be wrong about the better way, though. It's just that 127/64 is a pretty nice number.

97  is  a prime  number

Whenever  we  have  a  fraction with a prime  number  in the  denominator, we will  get  a repeating  decimal

{0.3196  is  a terminating decimal  ]

A rectangle has length (x + 5)cm and width (x –2)cm. Its area is 60 cm^2.  What is x?    

Length times Width equals Area.  So,                     (x + 5)(x – 2) = 60  

Multiply it out and subtract 60 from both sides        x² + 3x – 10 – 60  =  0  

                                                                                x² + 3x – 70  =  0 

Factor it                                                                  (x + 10)(x – 7)  =  0

                                                                                 x = –10  and  x = 7  

You can't have a negative side so discard that one which leaves  x = 7   

_.

-4(x + 3)  ≤ -2  - 2x

-4x - 12 ≤  -2  -2x      

-4x + 2x  ≤  -2  + 12

-2x  ≤  10         divide  both sides  by -2, reverse the inequality  sign since we're dividing by a negative

x ≥  10   / -2

x ≥   - 5    {first  number line  shown }

This  is   DEFINITELY   tedious to solve  by  hand   !!!

I'll  do the set-up, but I'm  going to  rely on this website to do the "heavy-lifting"

https://matrix.reshish.com/gauss-jordanElimination.php

We have  this  system

a  +  b   +  c   +  d  +  e  + f + g    =  1

64 a  + 32b + 16c  + 8d  + 4e  + 2f + g  =  1/2

4096a  + 1024b + 256c +64d + 16e  + 4f + g   =1/4

262144a  + 32768b + 4096c  + 512d + 64e  + 8f + g  = 1/8

16777216a  +  1048576b  + 65536c + 4096d + 256e + 16f + g   =  1/16

1073741824a + 33554432b + 1048576c + 32768d+1024e  + 32f  + g   = 1/32

68719476736a  + 1073741824b + 16777216c  + 262144d+ 64f + g  = 1/64

We don't  need to worry  about  anything  but  the  answer  for  "g"   since  this will =  p(0)

And    "g"    = 127 /  64  =  p(0)

WHEW  !!!!

pls help @CPhill, @Melody and @anyone else!!!

If  we connect the  centers of the  bottom three circles, we  will form an equilatersl triangle  with sides  = 4

The  height of this triangle   =  sqrt (3) / 2  *   side length

And, by symmetry, we have  two  of  these triangles......so their  combined  heights   =  sqrt (3) * side length  = 

4sqrt (3) cm

And  the other  part  of the  total  height is  formed  by 2  radii of a circle  =  2 * 2  = 4  cm

So....the total  height =   4 ( sqrt (3)  + 1)  cm  ≈   10.928 cm

Let   the  exterior  angle  = x

Let the interior  angle =  2.5x 

So....the  sum of  an interior angle and its  exterior angle  = 180°

So.......

x  +  2.5x     =  180

3.5x  = 180

x = 180  / 3.5  = 360/7   =  the  exterior  angle

Since  the  sum  of the exterior angles of a polygon  =  360   the polygon must have  7  sides

The  sum of the  interior angles of the  quadrilateral  in the  center = 360°

Call these angles  A, B , C  and  D

And  each of these angles is supplemental to an exterior angle of a triangle

Call  these angles  (180 - A) , (180 - B) , (180 - C)  and (180  - D)

And by the exterior angle theorem, each  of these exterior  angles is equal to the  sum of the two remote  interior  orange angles  in  their respective triangles 

So....the  sum   of  all  the orange  angles =  (180 - A) + (180 - B)  + (180 - C) + (180 - D)  =

4(180)   - (A + B + C + D)   =

720   - 360   =

360°

If you flatten the block into a net drawing you will see going from A to B will  be

 sqrt ( (3+9)^2 + 5^2) = 13 cm

For  ease, move B to the origin

Then A  becomes  ( -2 + 1 , -1  -4)  =  ( -1 , -5)

The 90°  counterclock-wise rotation rule  is   x , y  →    -y  , x

So the new point for  the provisional  "A"   becomes  (5, -1)

And A'  becomes   (5 - 1, -1 + 4)  =  (4, 3)

Likewise... C  becomes  ( 5 + 1,  0 -4)  =  (6,-4)

And the new point for provisional "B"  becomes  (4, 6)

And C' becomes  ( 4 -1, , 6 + 4)  =  ( 3 , 9)

(a+b)(a-b) = a ^2  -b^2 

44  (a-b) - 704

(a-b = 704/44 = 16

a = adult

s = student = 3a

a + 3a = 472

a = 118     then   s = 3a = 354 tix

6.4 x 50000 = 320000 cm   =  3200 m = 3.2km

Call Pam's  rate  1 / x     where x  is the  hrs Pam takes by herself

Call Pete's rate   1 / (2x)     where 2x is the hrs Pete takes by himself  

Rate  * time  =  whole job done  ....so...

(1/x)((18)  +  1/  (2x) * 18  = 1

18/x   +  18/ (2x)    = 1

18/x   +  9/x  = 1

[ 18  + 9 ]   / x   =  1

27   =   x  =    no. of hours  that Pam takes  by herself

2(x)  = 2(27)   = 54  =  no. of  hours that Pete takes by himself

We have:

Ad + 2B = 4d + 6

Match the corresponding spots.

A = 4

B = 3

Put simply, multiply by the inverse.

\(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} = \frac{ad}{bc}\)

W = Fd

=  (40 N)(0.8 m/s * 1800  s)

= 57600 J

\(98\% = \frac{98}{100} = \frac{49}{50}\)