NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE explain thoroughly. Chapter 16
1 answer:
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Answer:
- complex plane; (cos(θ)+i·sin(θ))^n = cos(nθ) +i·sin(nθ)
- relationship between parameter and coordinates
- basically: (x, y) = (r·cos(θ), r·sin(θ)); can be solved for r, θ
Step-by-step explanation:
1. de Moivre's theorem (or identity) states that ...
It is a statement about powers of complex numbers, so is related to the complex plane.
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2. To graph a parametric equation, you need to know the relationship between the parameter and the coordinates you want to graph.
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3. Here are the relationships:
(x, y) = (r·cos(θ), r·sin(θ))
(r, θ) = (√(x² +y²), arctan(y/x)) . . . with attention to quadrant
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Answer: LAST OPTION.
Step-by-step explanation:
1. You have the following equation:
2. Then you must solve for x, as following:
Therefore, as you can see above, the answer for the exercise is the last option.
Answer:
Step-by-step explanation:
I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.
The position equation is
That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.
The first derivative of position is velocity:
v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):
0 = -3.72t + 15 and solve for t:\
-15 = -3.72t so
t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:
s(4.03) = -1.86(4.03)² + 15(4.03) so
s(4.03) = 30.2 meters.
Calculus is amazing. Much easier than most methods to solve problems like this.