Since the focus is at (0, 2) and directrix is y = -2
point where both of these have the same x-value will be at (0, 2) for the focus and (0, -2) for the directrix.
The vertex will also have the same x-value so it will be (0, y).
y-value is half-way between the y-value of the focus, and the y-value of the directrix at x = 0.
Directrix y-value is -2 at x = 0 and for the focus it's 2 at x = 0.
Halfway between y = -2 and y = 2 is y = 0.
So the vertex of the parabola occurs at (0, 0).
So that's x^2 = 4ay = 4(2)y = 8y.
y = 1/8*x^2
hope it helps
Answer:
The answer is: Y is always 2
Step-by-step explanation:
You can see this because as you go left to right the y corrodinate will always be 2 as the x increases/ decreases.
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
(5x-16)³-4=60
(5x-16)³=64
5x-16=4
5x=20
x=4
