Identify the values of the variables. give your answers in simplest radical form.

2 sqrt(3) = n

k = 4 sqrt(3)

Step-by-step explanation:

We know that cos 30 = adjacent/ hypotenuse

cos 30 = 6 /k

Multiply each side by k

k cos 30 = 6k * k

k cos 30 = 6

Divide each side by cos 30

k cos 30/ cos 30 = 6/ cos 30

k = 6 / cos 30

k = 6/ (sqrt(3)/2)

k =12 / sqrt(3)

We cannot leave the sqrt in the denominator

k = 12 / sqrt(3) * sqrt(3)/sqrt(3)

k = 12 sqrt(3)/3

k = 4 sqrt(3)

We know tan 30 = opposite/adjacent

                tan 30 = n/6

Multiply each side by 6

                  6 tan 30 = n

                  6 * (sqrt(3)/3) = n

                   6/3 * sqrt(3) = n

                    2 sqrt(3) = n

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

explanation:

step-by-step explanation: