91Ó°ÊÓ

\(31-42\) . Solve the equation both algebraically and graphically. $$ x^{2}+3=2 x $$

Find an equation of the line that satisfies the given conditions. Through \((-2,-11) ;\) perpendicular to the line passing through \((1,1)\) and \((5,-1)\)

\(37-40\) An equation and its graph are given. Find the \(x\) - and \(y\) -intercepts. $$ \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 $$

Aerodynamic Lift The lift \(L\) on an airplane wing at take-off varies jointly as the square of the speed \(s\) of the plane and the area \(A\) of its wings. A plane with a wing area of 500 \(\mathrm{ft}^{2}\) traveling at 50 \(\mathrm{mi} / \mathrm{h}\) experiences a lift of 1700 \(\mathrm{Jb}\) . How much lift would a plane with a wing area of 600 \(\mathrm{ft}^{2}\) traveling at 40 \(\mathrm{mi} / \mathrm{h}\) experience?

Plot the points \(P(5,1), Q(0,6),\) and \(R(-5,1)\) on a coordinate plane. Where must the point \(S\) be located so that the quadrilateral \(P Q R S\) is a square? Find the area of this square.

(a) Sketch the line with slope \(\frac{3}{2}\) that passes through the point \((-2,1)\) . (b) Find an equation for this line.

Drag Force on a Boat The drag force \(F\) on a boat is jointly proportional to the wetted surface area \(A\) on the hull and the square of the speed \(s\) of the boat. A boat experiences a drag force of 220 lb when traveling at 5 mi/h with a wetted surface area of 40 \(\mathrm{ft}^{2}\) . How fast must a boat be traveling if it has 28 \(\mathrm{ft}^{2}\) of wetted surface area and is experiencing a drag force of 175 \(\mathrm{lb} ?\)

\(37-40\) An equation and its graph are given. Find the \(x\) - and \(y\) -intercepts. $$ x^{4}+y^{2}-x y=16 $$

\(31-42\) . Solve the equation both algebraically and graphically. $$ 16 x^{4}=625 $$

Which of the points \(A(6,7)\) and \(B(-5,8)\) is closer to the origin?