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Sorry, EP....didn't see that you were answering this, as well

b / sin 24 =  12.9 / sin 108      multiply both sides by  sin 24

b =  12.9 sin 24  / sin 108 ≈   5.52 m

12.9/sin 108   =  b/sin24

sin 24  12.9/sin108 = b = 5.52 m

Write  s   as   4t^(-2)

The velocity is the derivative  of the displacement function...so

s' (t)  =  -8t^(-3)

When t = a......the velocity is

s ' (a)  =  -8(a)^(-3)

The derivative of the displacement (or position) equation is the velocity function

   (then the NEXT deriviative is the acceleration function......just an FYI)

s = 4/t^2 = 4 t^-2

s ' = v = -8 t^-3             sub in t = a

        v at t= a  = -8 a^-3 = -8/a^3

Anytime!! Need any more help just message me.

Oh yes it does work Thanks.

2.5

Thanks CPhill.

Good job, ILP   !!!!

I mean check your answer. If not the problem is done

3(2x-4)-4x+7<9

6x - 12 - 4x + 7 < 9

2x - 5  < 9      add 5 to both sides

2x < 14           divide both sides by 2

x < 7

how?... im new

SS do you need to check? 

First one....

Note at 0  sec, height = 0

At 1.5 sec...it has reached its highest point and returns to its resting position

At 3.0....it has reached its lowest point and back to its resting position

So....3 seconds

Second one

At 0.5 seconds....it's at the resting position

At 1 sec...it reaches its highest point

At 1.5 sec...it is back at the resting position

So   1.5 - 0.5  =   1 second

Third one

March means that  x = 3

So.....12.2 cos (3.14 * 3 / 6) + 54.9   = 54.9°

Last one

The minimum value for the cosine is -1

So....the lowest temperature is

23.7 (-1) + 18 =   -5.7°

Solving for x=

6x-12-4x+7 <9

2x-5 <9

X could be any number between 6.99 repeating -----> negetive infinity = X

3+2x+8 

-3      -3               you subtract 3 from both sides. get 2x=5 then divide by 2 that is how i got x=2.5.

----------

2x=5

2x=5

2    2

x=2.5

I'm assuming that this is

a_n = (2/5)(5)^(n - 1)

Recursive rule

a_n  =  a_n-1 *  (5),   where a₁ =  (2/5)

x           y

1          7

2          6

3          5

4          4

5          5

6          6

7          7             etc.

An ant moves on the following lattice, beginning at the dot labeled A.
Each minute he moves to one of the dots neighboring the dot he was at, choosing from among its neighbors at random.
What is the probability that after 5 minutes he is at the dot labeled B ?

My attempt:

\(\begin{array}{|r|r|r|} \hline & \text{path} & \text{probability} & \text{probability} \\ \hline 1& 3,2,3,2,3,&0.0039062500 \\ 2& 3,2,3,4,3,&0.0039062500\\ 3& 3,2,3,7,3,&0.0019531250\\ 4& 3,2,3,1,3,&0.0078125000 \\ 5& 3,2,6,2,3,&0.0039062500 \\ 6& 3,2,6,7,3,&0.0019531250 \\ 7& 3,4,3,2,3,&0.0039062500 \\ 8& 3,4,3,4,3,&0.0039062500 \\ 9& 3,4,3,7,3,&0.0019531250 \\ 10& 3,4,3,1,3,&0.0078125000 \\ 11& 3,4,8,4,3,&0.0039062500 \\ 12& 3,4,8,7,3,&0.0019531250 \\ 13& 3,7,3,2,3,&0.0019531250 \\ 14& 3,7,3,4,3,&0.0019531250 \\ 15& 3,7,3,7,3,&0.0009765625 \\ 16& 3,7,3,1,3,&0.0039062500 \\ 17& 3,7,6,2,3,&0.0019531250 \\ 18& 3,7,6,7,3,&0.0009765625 \\ 19& 3,7,8,4,3,&0.0019531250 \\ 20& 3,7,8,7,3,&0.0009765625 \\ 21& 3,7,11,7,3,&0.0009765625 \\ 22& 3,1,3,2,3,&0.0078125000 \\ 23& 3,1,3,4,3,&0.0078125000 \\ 24& 3,1,3,7,3,&0.0039062500 \\ 25& 3,1,3,1,3,&0.0156250000 \\ 26& 6,2,3,2,3,&0.0039062500 \\ 27& 6,2,3,4,3,&0.0039062500 \\ 28& 6,2,3,7,3,&0.0019531250 \\ 29& 6,2,3,1,3,&0.0078125000 \\ 30& 6,2,6,2,3,&0.0039062500 \\ 31& 6,2,6,7,3,&0.0019531250 \\ 32& 6,5,6,2,3,&0.0078125000 \\ 33& 6,5,6,7,3,&0.0039062500 \\ 34& 6,7,3,2,3,&0.0019531250 \\ 35& 6,7,3,4,3,&0.0019531250 \\ 36& 6,7,3,7,3,&0.0009765625 \\ 37& 6,7,3,1,3,&0.0039062500 \\ 38& 6,7,6,2,3,&0.0019531250 \\ 39& 6,7,6,7,3,&0.0009765625 \\ 40& 6,7,8,4,3,&0.0019531250 \\ 41& 6,7,8,7,3,&0.0009765625 \\ 42& 6,7,11,7,3,&0.0009765625 \\ 43& 6,10,6,2,3,&0.0039062500 \\ 44& 6,10,6,7,3,&0.0019531250 \\ 45& 6,10,11,7,3,&0.0019531250 \\ 46& 8,4,3,2,3,&0.0039062500 \\ 47& 8,4,3,4,3,&0.0039062500 \\ 48& 8,4,3,7,3,&0.0019531250 \\ 49& 8,4,3,1,3,&0.0078125000 \\ 50& 8,4,8,4,3,&0.0039062500 \\ 51& 8,4,8,7,3,&0.0019531250 \\ 52& 8,7,3,2,3,&0.0019531250 \\ 53& 8,7,3,4,3,&0.0019531250 \\ 54& 8,7,3,7,3,&0.0009765625 \\ 55& 8,7,3,1,3,&0.0039062500 \\ 56& 8,7,6,2,3,&0.0019531250 \\ 57& 8,7,6,7,3,&0.0009765625 \\ 58& 8,7,8,4,3,&0.0019531250 \\ 59& 8,7,8,7,3,&0.0009765625 \\ 60& 8,7,11,7,3,&0.0009765625 \\ 61& 8,9,8,4,3,&0.0078125000 \\ 62& 8,9,8,7,3,&0.0039062500 \\ 63& 8,12,8,4,3,&0.0039062500 \\ 64& 8,12,8,7,3,&0.0019531250 \\ 65& 8,12,11,7,3,&0.0019531250 \\ 66& 11,7,3,2,3,&0.0019531250 \\ 67& 11,7,3,4,3,&0.0019531250 \\ 68& 11,7,3,7,3,&0.0009765625 \\ 69& 11,7,3,1,3,&0.0039062500 \\ 70& 11,7,6,2,3,&0.0019531250 \\ 71& 11,7,6,7,3,&0.0009765625 \\ 72& 11,7,8,4,3,&0.0019531250 \\ 73& 11,7,8,7,3,&0.0009765625 \\ 74& 11,7,11,7,3,&0.0009765625 \\ 75& 11,10,6,2,3,&0.0039062500 \\ 76& 11,10,6,7,3,&0.0019531250 \\ 77& 11,10,11,7,3,&0.0019531250 \\ 78& 11,12,8,4,3,&0.0039062500 \\ 79& 11,12,8,7,3,&0.0019531250 \\ 80& 11,12,11,7,3,&0.0019531250 \\ 81& 11,13,11,7,3,&0.0039062500& \text{sum } = 0.2500000000 \\ \hline \end{array}\)

The probability that after 5 minutes he is at the dot labeled B is \(0.25\ (25\ \%)\)

Sorry....missed the 'equilateral'   part

area of equilateral triangle = (sqrt 3)  /4    * a^2

                                             = sqrt 3 /4   *  10^2  = 25 sqrt 3

deleted

                        a^2       +4     - 17/(a+2)    

a+2  |    a^3 +2a^2 +4a -9

             a^3 +2a^2

________________________

            0     +0        +4a-9

                                 4a+8

_________________________

                                  0 -17 R

2 Graph 

1  What do you SEE as the lowest point on the graph???    Y=

2 

3  REFLECTING across the x axis means multiplying by -1      -cos x

      shifting it 2 units DOWN means subtracting 2     

              -cos (x) -2

1  Amp = 3/4   from the equation

2 Midline of cos is USUALLY at y = 0    this one is shifted UP by 5

3 frequency =  2/2pi = 1/pi

4 the wave takes 8pi to make one complete up and down cycle    period = 8pi