Find all points of intersection of the given curves. (Assume 0 ≤ θ < 2π and r ≥ 0. Order your answers from smallest to largest θ. If an intersection occurs at the pole, enter POLE in the first answer blank.) r = 1 + cos(θ), r = 1 − sin(θ)

The points are (3π/4, ) and (7π/4, )

Step-by-step explanation:

Since the two equations r = 1 + cos(θ) and r = 1 − sin(θ) intersect, then

1 + cos(θ) = 1 − sin(θ)

collecting like terms

cos(θ) + sin(θ) = 1 - 1

cos(θ) + sin(θ) = 0

dividing through by cos(θ), we have

cos(θ)/cos(θ) + sin(θ)/cos(θ) = 0/cos(θ)

1 + tan(θ) = 0

tan(θ) = -1

Since tanθ is negative in both the second and fourth quadrant, we have

tan(π - θ) = 1 or tan(2π - θ) = 1

(π - θ) = tan⁻¹1 or (2π - θ) = tan⁻¹1

(π - θ) = π/4 or (2π - θ) = π/4

θ = π - π/4 = 3π/4 or θ = 2π - π/4 = 7π/4

Substituting these values into r = 1 + cos(θ), we have

r = 1 - cos(3π/4) or r = 1 - cos(7π/4)

r = 1 - (-1/√2) or r = 1 - 1/√2

r = 1 + √2/2 or r = 1 - √2/2

r = or r =

So, the points are (3π/4, ) and (7π/4, )

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic