The polar coordinate of any point can be written as:
(r, θ) = (r, θ + 2nπ) when positive
(r, θ) = [ - r, θ + (2n + 1)π ] when negative
The polar coordinates of this given point P is: P = (r, θ) = (5, π/3).
When the value of r is positive, the polar coordinate is written as P= (5, π/3) = (5, π/3 + 2nπ)
When the value of r is negative, the polar coordinate is written as P = (5, π/3) = [ - 5, π/3 + (2n + 1)π] where n is any integer.
Therefore all polar coordinates of point P are (5, π/3 + 2nπ) and [ - 5, π/3 + (2n + 1)π ].
Let w and 2w-5 be the width and length, respectively, of the rectangle. Then:
w(2w-5)=52
2w²-5w-52=0
(2w-13)(w+4)=0
w=13/2 or -4
The rectangle is 6.5 ft by 8 ft. ☺☺☺☺
204/6 = 34 trees a day. 340-204 =136 trees left to plant. 136/34 = 4 4 days
Answer:
Long diagonal: 12.12 yd
Short diagonal: 7 yd.
Step-by-step explanation:
As you can see, 4 righ triangles are formed.
The larger diagonal divides the angle ∠AFM=60° into two angles of 30° each.
Then, choose one the triangles that has the angles of 30°. The hypotenuse will be the side lenght of 7 yards, the long diagonal (D) will be twice the adjacent side and the short diagonal (d) will be twice the opposite side.
Then:
- Long diagonal:
![\frac{D}{2}=7*cos(30\°)=6.06yd\\\\D=2(\frac{D}{2})=2(6.06yd)=12.12yd](https://tex.z-dn.net/?f=%5Cfrac%7BD%7D%7B2%7D%3D7%2Acos%2830%5C%C2%B0%29%3D6.06yd%5C%5C%5C%5CD%3D2%28%5Cfrac%7BD%7D%7B2%7D%29%3D2%286.06yd%29%3D12.12yd)
- Short diagonal:
![\frac{d}{2}=7*sin(30\°)=3.5yd\\\\d=2(\frac{d}{2})=2(3.5yd)=7yd](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B2%7D%3D7%2Asin%2830%5C%C2%B0%29%3D3.5yd%5C%5C%5C%5Cd%3D2%28%5Cfrac%7Bd%7D%7B2%7D%29%3D2%283.5yd%29%3D7yd)