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S_A_V [24]
2 years ago
6

Find all polar coordinates of point P where P = ordered pair 6 comma negative pi divided by 5.

Mathematics
2 answers:
Rudik [331]2 years ago
8 0

Answer:

All polar coordinates of point P are (6,-\frac{\pi}{5}+2n\pi) and (-6,-\frac{\pi}{5}+(2n+1)\pi), where n is an integer.

Step-by-step explanation:

The given point is

P=(6,-\frac{\pi}{5})

If a point is P=(r,\theta), then all polar coordinates of point P are defined as

(r,\theta)=(r,\theta+2n\pi)

(r,\theta)=(-r,\theta-(2n+1)\pi)

where n is an integer.

In the given point r=6 and \theta=-\frac{\pi}{5}. So all polar coordinates of point P are defined as

(6,-\frac{\pi}{5})=(6,-\frac{\pi}{5}+2n\pi)

(6,-\frac{\pi}{5})=(-6,-\frac{\pi}{5}+(2n+1)\pi)

Therefore all polar coordinates of point P are (6,-\frac{\pi}{5}+2n\pi) and (-6,-\frac{\pi}{5}+(2n+1)\pi), where n is an integer.

Allushta [10]2 years ago
6 0

Answer:

P(6,-π/6) = (6, -π/6 + 2nπ) and P(-6,-π/6) = (-6, -π/6 + (2n+1)π)

Step-by-step explanation:

We need to find all polar coordinates of

P = (6,\frac{-\pi }{6})

The polar coordinates of any point can be reresented by (r,Ф)

where

(r,Ф) = (r, Ф+2nπ) where n is any integer and r is positive

and

(r,Ф) = (-r, Ф+(2n+1)π) where n is any integer and r is negative.

So, in the question given, r = 6 and Ф = -π/6

So, Polar coordinates will be:

P(6,-π/6) = (6, -π/6 + 2nπ) where where n is any integer and r is positive

and

P(-6,-π/6) = (-6, -π/6 + (2n+1)π) where n is any integer and r is negative.

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Flights arriving to DTW might be national or international. Assume that one out of every five national flights is followed by an
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Answer:

1/15

Step-by-step explanation:

Given

1 out of every 5 national flight is followed by an international flight.

p = 1/5

q = 1 - p

q = 1 - 1/5

q = 4/5

π0 = 0.25

We want to determine

p:the fraction of international flights that are followed by a national flight.

Let X = 0

If the nth flight is national

Let X = 1

if the flight is international

This gives rise to a two state Markov chain with transition probability as follows

P = (4/5. 1/5. p. 1-p)

The long run proportion are the below solution gotten from the Markov chain above

π0 = 4/5π0 + pπ1 ----- 1

π1 = 1/5π0 + (1 - p)π1---- 2

π0 + π1 = 1 -----------. 3

Solving the above equations,

We have

Substitute 0.25 for π0 in (3)

0.25 + π1 = 1

π1 = 1 - 0.25

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Solving 1 and 3

Substitute 0.75 for π1 and 0.25 for π0 in (1)

0.25 = 4/5 * 0.25 + 0.75p

0.25 = 0.2 + 0.75p

0.75p = 0.25 - 0.2

0.75p = 0.05

p = 0.05/0.75

P = 1/15 or 0.0667(6.67%)

So, one out of every 15 international flights is followed by a national flight (or 6.66 percent)

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3 years ago
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