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, )

step-by-step explanation:

in which figure is point g a centroid

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !