Consider the system of differential equations below: dx dt dy dt = = x-x²-xy y-y² where you may assume that x > 0 and y ≥ 0. - 1 2 xy
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- Don't use chat gpt Chatgpt means downvote1/3 SS For the given vectors V₁ and V₂ of Prob. 1/2, de- termine the magnitude of the vector difference V' =V₂ - V₁ and the angle, which V' makes with the positive x-axis. Complete both graphical and algebraic solutions.Vector A= -6i+4j Vector B= -3i-8j How do you find the quantity of abs(A+B)?
- For a short time, the speed v of a car, in m / s, is given by v = at2 + bt3, where t is the time in seconds. The units of a and b are, respectively, a) m/s^2; m/s^3 b) m/s^4; m/s^5 c) s^3/m; s^4/m d) m.s^2; m.s^4 e) m/s^3; m/s^4If only one answer is correct, would it be A or C? Or could both be correct? Please explain.d²y Let 4 - 5y = 0, suppose the solution has the form y = e1x. - dx2 dx Find the Characteristic Equation of å and find the roots of the equation.
- ū u = (-4,-8) Find the magnitude of u. Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth. ||ū|| =The Scalar Product The vectors A andB are given by A = 31 + 1j and B = -1î + 1j. (a) Determine the scalar product A - B. SOLUTION Conceptualize There is no physical system to imagine here. Rather, it is purely a mathematical exercise involving two (vectors Categorize Because we have a definition for the scalar product, we categorize this example as a substitution vy problem. Substitute the specific vector expressions for A and B: A-B = (31 + 1j) - (-1î + 1j) = [3i - (-1)i - [31 - 15 - 13 - (-1) + [1j - 15] The same result is obtained when we use the equation A -B = AB, + A8, + A,B, directly, where A, = 3, A, = 1, B, = -1 and 8, = 1. (b) Find the angle e between A and B. SOLUTION Evaluate the magnitudes of A and B using the Pythagorean theorem: A = VA,? + A, = B = V82 + B 2 = Use the equation A - B = AB cos(e) and the result from part (a) to find the angle (in degrees). cos(e) = AB EXERCISE As a particle moves from the origin to (7i + 5j) m, it is acted upon by a force given by (7î +…where a 0, to find the a and B, such that y = ax + B. Your answers should be expressed in terms of a and b. α Eliminate the parameter t from the set of parametric equations. x = at + b y = 2t - 1 В