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- Consider the Squirrel-Coyote system given by S' = 2S-4SC C' = SC-C (1) Sketch the nullclines of the system and label them (as S- or C-nullclines). Add arrows to each nullcline and each distinct region of the phase plane to indicate the direction of the vector field there. (No need to draw the whole vector field, just a single arrow to show direction in each significant place.)Find the domain of the vector function 7 (= t+7 Domain: {tLet W be the work (against the Sun’s gravitational force) required to transport an 80-kg person from Earth to Mars when the two planets are aligned with the Sun at their minimal distance of 55.7 × 106 km. Use Newton’s Universal Law of Gravity (see Exercises 35–37 in Section 6.5) to expressW as an integral and evaluate it. The Sun has massMs = 1.99×1030 kg, and the distance from the Sun to Earth is 149.6×106 km.100 identical balls are rolling along a straight line. They all have speed equal to v, but some of them might move in opposite directions. When two of them collide they immediately switch their direction and keep the speed v. What is the maximum number of collisions that can happen? Let f(w) be a function of vector w Є RN, i.e. f(w) = 1+e Determine the first derivative and matrix of second derivatives off with respect to w. Let A Є RN*N be a symmetric, positive definite matrix and bЄ RN a vector. If x ER, evaluate the integral Z(A,b) = e¯xAx+bx dx as a function of A and b. John throws a fair die with faces labelled 1 to 6. ⚫ He gains 10 points if the die shows 1. ⚫ He gains 1 point if the die shows 2 or 4. • No points are allocated otherwise. Let X be the random variable describing John's gain at each throw. Determine the variance of X.Find the DFT of [1, 2, 0].If A = yz(^2) i - 3xz(^2) j + 2xyz k , B = 3x i + 4z j - xy k and ∅= xyz , find (a) Ax (∇∅), (b) (Ax ∇) ∅, (c) (∇x A) x B, (d) B. ∇x A.dy Let dt Draw a direction field with 9 points to justify your answer. a 2t² + 3y + 1. Which of the following shows a trajectory through (0, 1)? aDetermine which of the following pairs of functions are linearly independent. NO_ANSWER f(x) = e5x NO_ANSWER f(t) = et cos(µt) NO_ANSWER cos (30) f(0) = 2 NO_ANSWER f(x) = x³ 9 ◆ 1. g(x) = e5(x-3) 9 9 2. g(t) = et sin(ut),μ‡0 3. g(0) = 20 cos³ (0) – 15 cos(0) - 4. 3 g(x) = |x|³Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t > 1 a new node is added to the network. The node arrives together with m = 2 new links, which are connected to m = 2 different nodes already present in the network. The probability II, that a new link is connected to node i is: N(t-1) II¿ = ki - 1 Ꮓ with Z=(k-1) j=1 where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at timet - 1.SEE MORE QUESTIONS