CPhill

You're on the right track....we have a pattern that you found as

Term    1   2   3    4   5   6   7    8    9  10   11  12   13    14  15  16

           3, 27, 24, 3, 21, 18, 3, 15, 12, 3,    9,   6,     3,   [3,    0,   3] , [ 3, 0, 3], ]3, 0 , 3]

Notice that......starting with the  14th term   we  have  the repeating pattern   3,0,3

Notice that   after  this    ( term   number + 2)   ] / 3       gives us  what we need  to determine the 2016th term

Notice  that

(14 + 2) / 3  =  16/3 =    5  +   1/3    =    1st   number  in the pattern  =  3

(15 + 2) / 3  =   17/3  =  5   +  2/3  =       2nd number in the pattern  =  0

(16 + 2) / 3  = 18/3  =    6        whole number   result gives us the 3rd number in the pattern   = 3

So....to determine the  2016th   term we have

(2016 + 2 ]   / 3   =  2018 / 3  =    =   672  + 2/3   =  2nd number in pattern  =   0

See  here, piano123  :

https://web2.0calc.com/questions/solve-this-with-good-explaination-please

Call   a, b  the legs  and the  hypotenuse, c

a + b +  c   = 60

a +  b =   60 - c                square both sides

a^2  + 2ab + b^2   =   3600 - 120c + c^2

Note   a^2 + b^2  = c^2

So....we have that

2ab  = 3600  - 120c

ab  =  1800 - 60c     (1)

Area of  triangle   = (1/2)  ab

Also

Area =   (1/2)c *12       so

(1/2)ab = (1/2) 12c

ab  =  12c        (2)        sub  (1)  into (2)

1800  - 60 c  =  12c

1800  =  72c

c = 25

a + b =   60  - c

a + b  =  60 -  25

a + b  =  35  =   sum of the leg lengths

2^x   =  9

27^y  =   2

Rewrite  as

x =   log 9/log 2 =     log 3^2  /  log 2   =    2log 3  / log 2

y =  log 2 / log 27      =    log 2 / log 3^3  =   log 2  / {3 log 3 ]

So

xy  =        2log 3 / log 2    *   log 2  / [ 3 log 3 ]    =   2/3

Maybe you meant   x - 5y  =  -7     ???

If so....rearrange as

-5y  =  -x - 7          divide  both sides by   -5

y = (1/5) + 7/5

The slope of this line   =   1/5

A perpendicular line has the slope   -  5

Rearrange     15x + Py   = Q     as

Py   =   -15x  +   Q         

y  =   (-15/P)x  +   Q/P     

To  have a slope of  -5,  P  must  be  =  3 

So   we have     

y =  -5x  +  Q/3

And since  (8,3)   is on this line we have that

3 = -5(8)  + Q/3

3   = -40  +  Q/3

43  =  Q/3          multiply through by 3

129 =   Q

So   (P,Q)   =   (3, 129)

125% =  1.25

"Of" means "Multiply"

So

1.25n   =30       divide both sides  by 1.25

n = 30/1.25   =   24

25%   =   .25 =  25/100 =  1/4

So

(1/4)  of 24   =    24 (1/4)   =    6

He reaches a min height  in      5/(2*1) =  2.5 s

So    the min height is

(2.5)^2  - 5(2.5) + 29    =  22.75 ft  =   23 ft

radius of  circle =   31000  light years

Number of  m  in one light year  =    3 * 10^8 / s  *  (3600 * 24 * 365)s   = 9.4608 * 10^15   m

Converting this to km   (divide by 10^3)  =   9.4608 * 10^12  km   in one light year

So   .....radius of this  circle =   31,000 * 9.4608 * 10^12 km  = 2.932848 * 10^17 km

Total distance  traveled by planet in one orbit =  2pi * r =   2 pi * 293.2848 * 10^17km

Convert  286,000,000 years  to hrs =   286,000,000  * 24 * 365  = 2.50536 * 10^12  hrs 

So....the speed is

D / T  =         [ 2pi * 293.2848*10^17] km  /  [ 2.50536 * 10^12  ]hr    ≈ 7.36 * 10^7   km/hr

What is the  method of solving this  ???

The center of  the  x^2 + y^2 + 1  =  (0,0)

The  radius of  Gamma  =   ( a + 2)  =  r

The distance  from (16,a)  to (0, 0) =  (r + 1)  =   ( a + 2 + 1) = (a + 3) 

16^2  +  a^2   =  ( a+ 2 + 1)^2

256 + a^2  =  (a + 3)^2

256  + a^2  =   a^2  + 6a  +  9

6a  =  247

a = 247/6

See the graph here  : https://www.desmos.com/calculator/l9klwgdmus