8. Consider the following model for the populations of two species in competition in a given environment at time t (for instance, lions and hyenas). Here, r(t) represents the number of hundreds of species X at time t, and y(t) represents the number of hundreds of species Y. =x-x²_ =y-y² dx dt dy dt 1 2 ty 1 2xy (a) Use the framework of #5 to do a phase plane analysis of this system. ii. x(0) = 1, y(0) = 1. - (b) For each of the initial conditions given below, describe how the sizes of the populations of X and Y change with time and what happens in the long run. i. x(0) = 2, y(0) = 0. iii. x(0) = 1, y(0) = 1. (From the phase plane analysis only, we cannot determine the exact shape of the trajectory. Draw two possibilities on your sketch. Is there more than one possibility

Q: Solve the following equation involving inverse trig Sin^-1 (theta)+tan^-1 (theta)=0

A:

Q: What is the real number equivalent for sin ( Cos ^ -1 ( 1/2)) ?

A:

Q: which one of the following is the same as sin(tan^-12/x) a. x/sqrt x^2+4 b. 2/sqrtx^2+4 c. sqrt…

A:

Q: Solve the equation 2sin^2 x = 2 + cosx. Determine the solutions on the interval [0,2pi]

A:

Q: 2-5cos@ do sin e

A: Given integration is: ∫2-5cosθsinθdθ To find the value of integration.

Q: Why is cos(sin^-1(x)) equal to sqrt(1-x^2)?

A:

Q: Graph the equation r = sin^2 (2.3u) + cos^4 (2.3u) for 0 <=u<= 10pai.

A:

Q: Use the reduction formulas to reduce sin^4 θ to only linear powers of cosine (cos(θ) = ”linear”,…

A:

Q: differentiate y = sin^3(tet^2) and simplify

A: The given function is y=sin3tet2We have to differentiate with respect to t…

Q: Solve the equation for all solutions in the interval. Write answer in radians: tan^4…

A: