Chapter 12: Problem 42
Decide whether the ordered pair is a solution of the inequality. $$y \leq 2 x^{2}-3 x+10 ;(-2,20)$$
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Decide whether the ordered pair is a solution of the inequality. $$y \geq 2 x^{2}-8 x+8 ;(3,-2)$$
For what values of the variable is the rational expression undefined? $$\frac{x+2}{x^{2}-4}$$
Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{3 x-2}=4-x$$
Use the following information. A ride at an amusement park spins in a circle of radius \(r\) (in meters). The centripetal force \(F\) experienced by a passenger on the ride is modeled by the equation below, where \(t\) is the number of seconds the ride takes to complete one revolution and \(m\) is the mass (in kilograms) of the passenger. $$t=\sqrt{\frac{4 \pi^{2} m r}{F}}$$ A person whose mass is 67.5 kilograms is on a ride that is spinning in a circle at a rate of 10 seconds per revolution. The radius of the circle is 6 meters. How much centripetal force does the person experience?
Solve the equation. Check for extraneous solutions. $$x=\sqrt{\frac{3}{2} x+\frac{5}{2}}$$
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