91Ó°ÊÓ

Use algebraic, graphical, or numerical methods to find all real solutions of the equation, approximating when necessary. $$x^{5}-6 x+6=0$$

Red Riding Hood drives the 432 miles to Grandmother's house in 1 hour less than it takes the Wolf to drive the same route. Her average speed is 6 mph faster than the Wolf's average speed. How fast does each drive?

To get to work, Sam jogs 3 kilometers to the train and then rides the remaining 5 kilometers. If the train goes 40 kilometers per hour faster than Sam's constant rate of jogging and the entire trip takes 30 minutes, how fast does Sam jog?

Use algebraic, graphical, or numerical methods to find all real solutions of the equation, approximating when necessary. $$2 x-\frac{1}{2} x^{2}-\frac{1}{12} x^{4}=0$$

The dimensions of a rectangular box are consecutive integers. If the box has volume of 13,800 cubic centimeters, what are its dimensions?

Use algebraic, graphical, or numerical methods to find all real solutions of the equation, approximating when necessary. $$\frac{1}{4} x^{4}+\frac{1}{3} x^{2}+3 x-1=0$$

In Exercises \(31-36\), determine which of the following viewing windows gives the best view of the graph of the given equation (a) \(-10 \leq x \leq 10 ; \quad-10 \leq y \leq 10\) (b) \(-5 \leq x \leq 25 ; \quad 0 \leq y \leq 20\) (c) \(-10 \leq x \leq 10 ;-100 \leq y \leq 100\) (d) \(-20 \leq x \leq 15 ; \quad-60 \leq y \leq 250\) (e) None of \(a, b, c, d\) gives a complete graph.. $$y=x^{4}+x-5$$

In 2005 Dan Wheldon won the Indianapolis 500 (mile) race. His speed was 83 mph faster than the speed of Ray Harroun, who won the race in \(1911 .\) Wheldon took 3.53 hours less than Harroun to complete the race. What was Wheldon's average speed?

A homemade loaf of bread turns out to be a perfect cube. Five slices of bread, each .6 inch thick, are cut from one end of the loaf. The remainder of the loaf now has a volume of 235 cubic inches. What were the dimensions of the original loaf?

Find an exact solution of the equation in the given open interval. For example, if the graphical approximation of a solution begins. \(3333,\) check to see whether \(1 / 3\) is the exact solution. Similarly, \(\sqrt{2} \approx 1.414 ;\) so if your approximation begins \(1.414,\) check to see whether \(\sqrt{2}\) is a solution.) $$x^{3}+x^{2}-2 x-2=0 ; \quad(1,2)$$