(1 point) (a) the cartesian coordinates of a point are (1,1). (i) find polar coordinates (r,θ) of the point, where r> 0 and 0≤θ< 2π. r= θ= (ii) find polar coordinates (r,θ) of the point, where r< 0 and 0≤θ< 2π. r= θ= (b) the cartesian coordinates of a point are (23–√,−2). (i) find polar coordinates (r,θ) of the point, where r> 0 and 0≤θ< 2π. r= θ= (ii) find polar coordinates (r,θ) of the point, where r< 0 and 0≤θ< 2π.

P(1, π/4)

P(-1, π/4)

P(4, 5π/6)

P(-4, 5π/6)

Step-by-step explanation:

Knowing the formulas

r = √(x²+y²)

θ = Arctg (y/x)

we have

a) P(1, 1)

i)  

r = √(1²+1²) = +1

r = +1

θ = Arctg (1/1) = π/4

P(1, π/4)

ii) r = √(1²+1²) = -1

r = -1

θ = Arctg (1/1) = π/4

P(-1, π/4)

b) P(2√3, -2)

i)  

r = √((2√3)²+(-2)²) = +4

r = +4

θ = Arctg (-2/2√3) = 5π/6

P(4, 5π/6)

ii)

r = √((2√3)²+(-2)²) = -4

r = -4

θ = Arctg (-2/2√3) = 5π/6

P(-4, 5π/6)

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.