How do I graph y = 1/5 cos x

Find all polar coordinates of point P where P = ordered pair 3 comma negative pi divided by 3 .

jek_recluse [69]

Answer:

The all polar coordinates of P are:

(3 , -π/3) , (3 , 5π/3) , (-3 , 2π/3) , (-3 , -4π/3)

Step-by-step explanation:

* Lets study the polar coordinates of a point

- In polar coordinates there is an infinite number of coordinates

for a given point.

- The polar coordinates of a point (x , y) is (r , θ), where

r = √ ( x2 + y2 )

θ = tan-1 ( y / x )

# Ex: the following four points are all coordinates for the same point.

* (5 , π/3) = (5 , −5π/3) = (−5 , 4π/3) =(−5 , −2π/3)

- These four points only represent the coordinates of the point without

rotating more than once

- So the point (r,θ) can be represented by any of the following

coordinate pairs (r , θ + 2π n) and (−r , θ + (2n + 1) π), where n is

any integer.

* Now lets solve the problem

∵ P = (3 , -π/3)

∵ (r , θ + 2πn)

∴ r = 3 an d Ф = -π/3

- let n = 1

∴ P = (3 , -π/3 + 2π)

∴ P = (3 , 5π/3)

∵ P =(3 , -π/3)

∵ P = (-r , θ + (2n + 1) π)

Let n = 0

∴ P = (-3 , -π/3 + (2×0 + 1) π)

∴ P = (-3 , -π/3 + (0 + 1) π)

∴ P = (-3 , -π/3 + π)

∴ P = (-3 , 2π/3)

∵ P =(3 , -π/3)

∵ P = (-r , θ + (2n + 1) π)

Let n = -1

∴ P = (-3 , -π/3 + (2(-1) + 1) π)

∴ P = (-3 , -π/3 + (-2 + 1) π)

∴ P = (-3 , -π/3 + -π) = (-3 , -4π/3)

∴ P = (-3 , -4π/3)

5 0

2 years ago

2. Jolie manages an annual film festival in her town. Every year, one movie from every genre is chosen as a finalist to win best

Ad libitum [116K]

Answer:

Step-by-step explanation:

All votes: 10*3+18+22+15*3+20+8=143

143*0.2(20%)=28.6 about 28vote (Scifi)

Scifi, 10 adults, 18 children, which is 20% of the votes.

4 0

2 years ago

Mr. Vella can build a brick wall in 4 days. His apprentice can build the same wall in 6 days. After working alone for 3 days, Mr

Vitek1552 [10]

Mr. Vella can build the wall in 4 days, however only works on it for 3 days. That means that he has completed 75% of the and is leaving 25% for his apprentice.

We need to figure out how long it takes the apprentice to build 25% of a wall. We know he can build 100% of a wall in 6 days, so dividing 6 days by 4 will give us our answer.

6/4 = 3/2 = 1.5 days

It took the apprentice 1.5 days to finish the wall.

6 0

3 years ago

Two stores carry a simuler stereo for the same originail price of $573. One store offers a 16% discount and the second store sel

snow_tiger [21]

store number two gives a better discount .

if you go to store one and buy it for 573 with the 16% DISCOUNT, YOU GET 481.32, THEREFORE, STORE TWO IS BETTER(caps lock) also did store two have a discount?

3 0

3 years ago

The table below shows the temperature in degrees for eight consecutive days as well as the respective number of ice cream cones

cricket20 [7]

Answer:

We have to find the equation of least squares regression line in order to find the number of ice cream cones that the shopkeeper to sell if the temperature is 106 degrees. We can use excel regression data analysis tool to find the equation of the regression line. The excel output is attached here.

The equation of the least squares regression line is:

$\hat{y}=46.587+5.080x$

Now, if the temperature is 106 degrees, then the number of cones expected to be sold is given below:

$\hat{y}=46.587+5.080 \times 106$

$=585.1 \approx 585$

Therefore, the number of ice cream cones that the shopkeeper would expect to sell if the temperature is 106 degrees is 585.

6 0

3 years ago