Describe the curve defined by the vector function r(t) = 3 + t, 5 + 4t, −2 + 3t . solution the corresponding parametric equations are x = 3+t , y = 5 + 4t, z = −2+3t which we recognize from these equations as parametric equations of a line passing through the point (3, 5, −2) and parallel to the vector 1, 4, 3 . alternatively, we could observe that the function can be written as r = r0 + tv, where r0 = 3, 5, −2 and v = t⟨1, 4, 3⟩ , and this is the vector equation of a line as given by this equation.

Efficient homemakers ltd. makes canvas wallets and leather wallets as part of a money-making project. for the canvas wallets, they need two yards of canvas and two yards of leather. for the leather wallets, they need four yards of leather and three yards of canvas. their production unit has purchased 44 yards of leather and 40 yards of canvas. let x be the number of leather wallets and y be the number of canvas wallets. draw the graph showing the feasible region to represent the number of the leather and canvas wallets that can be produced.