CPhill

1. P(7)  = 0    [there isn't a "7" on a single die ]

2. P(Red) = [Number of red marbles] / [ Total number of marbles ]  =   1 / 7

sin^2θ/1-cosθ=1+cosθ   .......working with the left hand side, we have

(1 - cos^2θ) / (1 - cosθ)  =

[( 1 + cosθ) (1 - cosθ) ] / ( 1 - cosθ)  =

1 + cosθ

y = rs + t    .......

y = (3)(4) + 1  =   12 + 1  = 13

We have 18 marbles of which 6 are green.......the probability of drawing a green one is 6/18  = 1/3

N^2 - N - 90  = 0     factor

(N - 10) (N + 9)  = 0        setting each factor to 0, we have that N = 10 or N = -9

Here it is with synthetic division....

1       1   -1    1   -1   1   -4

               1    0    1   0    1

       --------------------------

        1     0    1    0   1   -3

The resulting polynomial   is   x^4 + x^2 + 1    with a remainder of  -3/(x - 1)

x = √[64 - 25] = √39

So  cos  = √39 / 64   and tan  = 5/√39

The  csc, sec and cot will be the reciprocals of the sin, cos and tan, respectively

Since the starting point is (-2, 9), the slope is -3/4, and t increases as x increases,  we have....

x(t) = -2 + 3t

y(t)  = 9 - 4t

Notice that when t = 1, x = 1 and y = 5

And the distance between the ponts is  √[(-2 -1)^2 + (9 - 5)^2] = √[3^2 + 4^2] = √25......which means that some object traveling on this line starting at (-2,9) and moving at this speed (per some time unit) will reach (1, 5)  after one of these time units.....just what we want....!!!

1250 revs  every 5 minutes = 250 revs every minute

x(t)  = 6.5cos[(-500pi)t]  

y(t)  = 6.5sin [(-500pi) t ]