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- Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the square of thedistance.A parabola has the equation y^2 = -4ax. Determine the slope of the orthogonal trajectories.Find the absolute maximum and minimum values of f(x, y) = x^2 +xy + y^2 - 3x + 3y on the triangular region cut from the first quadrant by the linex + y = 4.
- Find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =kThe number of walmart stores around the world in 2001 was 2,380 stores. By 2019, the number of stores had grown to 9,235. (a) Assuming Walmart's expansion grows linearly, find the linear model, y=mx+by=mx+b, representing the number of stores xx year since 2000.The population dynamics of many fish species (such as salmon) can be described by the Ricker curve: y=axe-bx, where a > 1 and b > 1 are constants, x is the size of the parental stock, and y is the number of offspring. Determine the size of the parental stock that maximizes the number of offspring. (Your answer will involve the constants a and b).
- A value of r close to _______ suggests at most a weak linear relationship between the variables.A desk lamp factory is willing to supply x lamps for a price, in dollars, of p(x) = 6x + 193, while consumers are willing to buy x lamps at a price, in dollars, of p(x) = −3x + 328. Determine the market equilibrium point. (x, y) =Determine the best (according to sum-of-squares-measure) curve y = Axb, through the dataabove.Transformed equation ln(y) = ln(A) + b ln(x)orY = a + bX.
- Find a direct variation model that relates y and x. x = 2, y = 1Determine the best (according to sum-of-squares-measure) curve y = Axb, through the data above. Transformed equation ln(y) = ln(A) + b ln(x) or Y = a + bX.Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to the point (0, 2).