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Remainder = 2

The sum of the sequence is 5270      5270 / 6 = 878 R 2

a = 13

I just used a calculator

sin theta =  cos 5 - sin 75

               =  .99619 -.96592

                = .0302688

arcsin (.0302688) = 1.7345 degrees

for the 600's there is 100 such numbers  (600 THRU 699)

  for each other 100 there are 20 such numbers (example   006  16  26 36 46 56 66  76 76 86 96 60 61 62 63 64 65     67 68 69) 

        000, 100, 200,300,400,500,700's

  100      +      7 x 20 = 240  numbers have at least one 6     

Cos C will equal Sin B

Find sin b

(3/25)² + sinb ² = 1

9/625 + sin^2 = 1

sin^2 = 616/625

sin b = cos c = sqrt(616)/25    simplify as needed.....

Add 3 to both sides:

$(x+1)(y+3)=118$

$118=2*59$

$x+1=2$

$y+3=59$

$x=1, y=56$

Vertex  (2,4) form of the parabola will be

y = a (x-2)^2 + 4          Now sub in the given point to calulate 'a'

-1 = a(-1-2)^2 + 4

a = -5/9

So your parabola is now  

  y = -5/9 (x-2)^2 + 4        expand to

           y = - 5/9 x^2 +  20/9 x  -20/9 + 4     simplify to get the requested form.....

See https://web2.0calc.com/questions/don-t-know-how-plz-help

a + b + c = 16.

x + x^2 + x^3 + . . . + x^2010 + x^2011 = 1.

The least possible value of b is 27.

h = 148

148 = -16t^2+137t+100     

-16t^2 +137t -48  = 0    Use Quadrtatic Formula to find the two values of 't'       a = -16     b = 137    c = -48

\(t = {-137 \pm \sqrt{137^2-4(-16)(-48)} \over 2(-16)}\)        compute on !

Can you show me how? I do not get it.

Not sure....is it just      5 +3 = 8 ?

(1)(g² +1)² +16     =    g⁴ + 2g² +17

the points (10, 10), (−14, 10)  show the axis of symmetry to be   -2    ( midway between 10 and -14)

  so the x coordinate of the vertex is -2         vertex = (-2,k)

Vertex form of the parabola

y = a (x+2)^2  +k     sub in the first point in the list

10 = a (12)^2 + k

10 = 144a + k

Sub in another point ( I'll use the third one)

7 = a (22)^2 +k

7 = 484a + k               Two equations with two unknowns <====== solve to find a = -3/340        k =   11 23/85

Your parabola becomes

y = -3/340 ( x+2)^2   + 11  23/85

Here is a confimational graph:

https://www.desmos.com/calculator/k2brpujphy

Start with f(x) = 8          where x , in this case is g(a)

f(x) = 8

x^2 + 8 = 8 

x = 0           rememeber   that x is g(a) in this case,    so   a^2 - 4 =0

a^2 - 4 = 0

a^2 = 4

a = +-2

A right-angled triangle has a perimeter of 1276 and the longest side of 533.  What is the length of the inradius?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

P = 1276          s = 1276 / 2           Hypotenuse c = 533

Short leg = a         long leg = b            a + b = 743

a² + (743 - a)² = c²

a = 308           b = 435

A = 1/2(ab)

Inradius     r = A / s = 105

(n +  2i)^4   =

n^4   +  4n^3 * 2i  +  6n^2 * (2i)^2  +  4n (2i)^3   +  (2i)^4      =

n^4   +  8n^3 i      + 24n^2 i^2       +  32n i^3   +   16i^4      =

n^4  + 8n^3 i   - 24n^2  -  32n i      +  16

The  terms in red will  always be integers for any integer  n

So

8n^3 i    -  32n i   =     0       (  we want to eliminate the  "i's"   )

8n i  ( n^2  - 4)  =  0

8n i  ( n + 2) ( n - 2)  =  0

This  will  be true when   n   =  0     n =  -2     and  n   =  2

inradius ,  r   for  a right triangle  =

[  sum  of two  leg  lengths  -  hypotenuse  ]    /   2

The  sum of  the two  leg lengths =   1276  -  533  =  743

So

r  =    [ 743  - 533  ]  /  2    =     210  / 2  =  105

No prob....glad to help   !!!!

Using  the  square of  the distance formula

(4 - 2a)^2   +  (a - 4 - 1)^2   =    (2sqrt 30) ^2           simplify

16  - 16a  + 4a^2  +  ( a - 5)^2  =    4*30

16 - 16a  +  4a^2  + a^2  - 10a  +  25 =   120

5a^2  -  26a  + 41   = 120

5a^2  - 26a   -  79   =   0

This will have two solutions for  "a".....their  product  =   -79 / 5

wow i was way off 😂

oh well 

thanks guys! 

Second  one

f  = 2x - 1   

g =  x^3

(f o g) (-3)     means  to  put  -3  into  "g" and  evalute....so...

(-3)^3   =  -27

And then , we put THIS result  into " f " ....so....

2 (-27)  - 1    = 

-54  -1  =

-55

1.    b +  4  = a

So

4  =   a  - b

And  note  that   (a - b)^2   = (b - a)^2

So

4^2  =  ( a - b)^2   = (b  - a)^2

So

16  =(b - a)^2