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Find all of the polar coordinates of point P if p=(1,-pi/6)

Mama L [17]

Answer:

The all polar coordinates of point P are (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n).

Step-by-step explanation:

The polar coordinates can be written as (r,Ф)= (r,Ф+2nn) or (r,Ф) =(-r,Ф+(2n+1)n) and n is any integer value.

We are given p=(1,-pi/6)

P(r,Ф), then r = 1 and Ф = -pi/6

The polar coordinates will be

P(r,Ф)= (r,Ф+2nn) = (1 , -pi/6 + 2nn) and n is any positive integer and the value of r is positive.

P(r,Ф) =(-r,Ф+(2n+1)n) = (-1, -pi/6+(2n+1)n) and n is any positive integer and the value of r is negative.

The all polar coordinates of point P are (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n)

6 0

2 years ago

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The flower shop sold roses and tulips. The number of roses sold was 5 less than twice the number of tulips sold. If the shop sol

LenaWriter [7]

Answer: the number of roses sold is 69 while number of tulips is 37

Step-by-step explanation:

Let x represent the number of roses that the flower shop sold.

Let y represent the number of tulips that the flower shop sold.

The number of roses sold was 5 less than twice the number of tulips sold. This means that

x = 2y - 5 - - -- -- - - - - - ;1

If the shop sold 106 flowers in total, it means that

x + y = 106

Substituting x = 106 - y into equation 1, it becomes

106 - y = 2y - 5

3y = 106 + 5 = 111

y = 111/3 = 37

x = 106 - y = 106 - 37

x = 69

7 0

2 years ago

Please be quick! I need this as soon as possible!

Tpy6a [65]

Answer:

6

Step-by-step explanation:

7 0

3 years ago

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The dot plot represents the prices of different brands of chocolate bars.

Gala2k [10]

The answer is simply C.$2.50

3 0

3 years ago

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Can someone help me please

aleksklad [387]

9514 1404 393

Answer:

IS a parallelogram

Step-by-step explanation:

The slope formula for the slope of the line between points (x1, y1) and (x2, y2) is ...

m = (y2 -y1)/(x2 -x1)

The distance formula for the length of that same line is ...

d = √((x2 -x1)^2 +(y2 -y1)^2)

Here, you're asked to use each of these formulas 4 times, once for each side of the quadrilateral. I find it convenient to let a calculator or spreadsheet do the repetitive calculations. The result is attached.

The attachment shows that opposites sides have the same length and slope, so are parallel. The quadrilateral is a parallelogram. (The two points used in each calculation are the ones on the result line and the line immediately below. That is why point B is copied to the end of the list.)

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<em>Additional comments</em>

There are much simpler ways to prove the figure is a parallelogram. My favorite is to add the coordinates of the end points of the diagonals:

B +D = (-2+6, -9-3) = (4, -12)

C +E = (0+4, -5-7) = (4, -12)

These values being the same demonstrates the midpoints of the diagonals are coincident. That will only be the case if the quadrilateral is a parallelogram.

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If you must use slope and distance formulas, showing either pair of opposite sides is parallel and have the same length is sufficient to guarantee that the other two sides are also parallel and have the same length. That is, the calculations required in this problem only need to be applied to one pair of opposite sides. (Using a spreadsheet, it's not a lot of extra work to do the calculations for both pairs of opposite sides.)

7 0

2 years ago