Find the expressions for x and y as function of t separately from the simulta- neous equations, dx dy 2. +2x+y = 11t, dt dt dx dy 2 +3 +5x-3y dt dt = 2.
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- Use a system of linear equation to find the parabola y=ax2+bx+c that passes through the points (1,2), (0,1) and (2,6)Determine the quadratic equation that best fits the given set of data: (1, 2), (2, 3), (4, 3), (6,4), (7, 8) 310 273 y=. - 318 91 318 91 310 -+- 91 318 21 310 273 x + ·x + x + 310 5 273 +x+ 21 5 -1-² 21 5 -1.² 273 5 =x² 21 318 91Explain why z2 = x + 3y is not a function of x and y.
- Find the equation of the line perpendicular to y=−2y= through the point (3,2)Consider the difference equation = Xn+1 Xn+bsin(2xn). Determine any fixed points of this difference equation and their stability as a func- tion of the parameter b.The path of flight (trajectory) of a football thrown by a quarterback is described by the +0) ². x² following function: y(x) = - where y = vertical position of football relative to the ground Linear model yo = vertical launch position of football relative to the ground horizontal position of football relative to launch position g=magnitude of gravitational acceleration vo = launch speed = launch angle relative to horizontal Which type of mathematical model is used here to describe the football's trajectory? Nonlinear model g 2v² cos² e Exponential model + (tan)x + yo Trigonometric model
- A duck's flight is given by the following expression: y = x^2 + x + 4. X and y are coordinates of its flight. When x = 2, the duck takes a hit and thereafter its flight follows the trajectory of a tangent line. What is the coordinate when x=4.Determine the equation of the line through (3,4) which forms the positive x and y axes, the triangle with the least area.