Answer:
See below in bold.
Step-by-step explanation:
cos 4x = 2cos^2 2x - 1 = 2 (2 cos^2 x - 1)^2 - 1
and cos 2x = 2 cos^2 x - 1 so we have:
2 ( 2 cos^2 x - 1)^2 - 1 - (2cos^2 x - 1) = 0
2 ( 2 cos^2 x - 1)^2 - 2 cos^2 x = 0
(2 cos^2 x - 1)^2 - cos^2 x = 0
Let c = cos^2 x, then:
(2c - 1)^2 - c = 0
4c^2 - 4c + 1 - c = 0
4c^2 - 5c + 1 = 0
c = 0.25, 1
cos^2 x = 0.25 gives cos x = +/- 0.5
and cos^2 x = 1 gives cos x = +/- 1.
So for x = +/- 1 , x = 0, π.
For cos x = +/- 0.5, x = π/3, 2π/3, 4π3,5π/3.
We will need to find the area of the circle. We will use this formula:
A =
![\pi](https://tex.z-dn.net/?f=%20%5Cpi%20)
* radius^2
The question says we will use 3.14 for
![\pi](https://tex.z-dn.net/?f=%20%5Cpi%20)
.
And we know radius is equal to 22.
A = 3.14 * 22^2
A = 3.14 * 484
A = 1519.76
Round to the nearest tenth.
A = 1519.8
So, the maximum area the sprinkler can water is <span>1519.8</span> ft squared.
EDIT:
I found a mistake in my answer.
Answer:
.
Step-by-step explanation:
The direct variation is defined as
where, k is constant of proportionality.
It is given that a direct variation function contains the points (-8,-6) and (12, 9).
Substitute x=-8 and y=-6 in the above equation.
Divide both sides by -8.
The value of constant of proportionality is
. So, the required equation is
At x=12,
It means, the line passing through (12,9). Hence, the equation is correct.
Therefore, the equation of the function is
.
Answer:
3 :)
Step-by-step explanation:
1/5 of 50% should be 10%.