Answer:
vertex: (5/6,5)
focus: (- 2/3, 5)
axis of symmetry: y = 5
directrix: x = 7/3
Step-by-step explanation:
use the vertex form to determine the values of a.h. and k and use these values to find the direction the parabola opnes, vertex, foucs, axis of symmetry, and directrix
THERE ARE 52 WEEKS IN A YEAR.
40 (hours) x 52 (weeks) = 2080
29460 / 2080 = 14.25
He made a. $14.25 per hour.
Answer:
40
Step-by-step explanation:
That is literally all there is to it
The first contract can go to any of 12 firms. The second can go to any of the remaining 11 firms, and so on. Finally, the 4th contract can go to any of the 9 firms that don't yet have a contract.
The number of ways the contracts can be awarded is
... 12×11×10×9 = 11,880
I will use the letter x instead of theta.
Then the problem is, given sec(x) + tan(x) = P, show that
sin(x) = [P^2 - 1] / [P^2 + 1]
I am going to take a non regular path.
First, develop a little the left side of the first equation:
sec(x) + tan(x) = 1 / cos(x) + sin(x) / cos(x) = [1 + sin(x)] / cos(x)
and that is equal to P.
Second, develop the rigth side of the second equation:
[p^2 - 1] / [p^2 + 1] =
= [ { [1 + sin(x)] / cos(x) }^2 - 1] / [ { [1 + sin(x)] / cos(x)}^2 +1 ] =
= { [1 + sin(x)]^2 - [cos(x)]^2 } / { [1 + sin(x)]^2 + [cos(x)]^2 } =
= {1 + 2sin(x) + [sin(x)^2] - [cos(x)^2] } / {1 + 2sin(x) + [sin(x)^2] + [cos(x)^2] }
= {2sin(x) + [sin(x)]^2 + [sin(x)]^2 } / { 1 + 2 sin(x) + 1} =
= {2sin(x) + 2 [sin(x)]^2 } / {2 + 2sin(x)} = {2sin(x) ( 1 + sin(x)} / {2(1+sin(x)} =
= sin(x)
Then, working with the first equation, we have proved that [p^2 - 1] / [p^2 + 1] = sin(x), the second equation.
