What are both the payoff and the profit or loss per share for an investor in the following twosituations?
i. Jean buys the June, 2022 expiration Paypal call option for $6.40 with an exercise priceof $120, if the Paypal stock price at the expiration date is $132?
ii. Joan buys a Paypal put option for $4.50 with the same expiration date and exerciseprice as Jean’s call option, and the Paypal stock price is also $132 at the expirationdate?

Consider a car that is moving up a hill while on cruise control. Denoting the force produced by the engine as the input, u(t), and the vehicle's speed as the output, y(t), we can model the vehicle as follows: v(t) = = - v(t) + [u(t) + d(t)] T m (1) (2) y(t) = v(t) + n(t) The mass of the car is m = 1000kg . The time constant of the system is 7 = 10s The gravitational constant is g = 9.81m/s The system is subject to a disturbance d(t) The speed measurement y(t) is corrupted by sensor noise n(t) For this problem, assume the following: The disturbance is given by d(t) = -mg sin(0) - av(t) The noise is given by n(t) = 0 . The initial condition is v(0) = 0m/s Do the following: (a) Let u(t) = 100. For 0 = 10 and a = 0.5kg/m, use MATLAB's ode45 function (or a Python equivalent) to integrate Eq. 1 over t [0, 30]s. Provide your code. (b) Provide plots for y(t) and d(t) for the conditions given in part (a). (c) Provide a qualitative explanation of the role 7 has on the output y(t). For example, set a = 0kg/m and 0 = 0, and experiment with different (positive) values of 7. (d) Set a = 750kg/m and 0 = 0. Simulate and plot y(t), 32(t), and y3(t) for u(t) = 100 sin(t), u2(t) = 100 sin(t), and u3(t) = u(t) + u(t). Additionally, plot y (t) + y2(t) on the same plot. Does y3(t) match y (t) + y2 (t)? (e) Repeat part (d) with a = 0kg/m. Does y3(t) match y (t) + y(t) in this case? Explain why this result differs from that in part (d).