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Chapter 0: Problem 143
If you are given two real numbers, explain how to determine which is the lesser.
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A football was kicked vertically upward from a height of 4 feet with an initial speed of 60 feet per second. The formula $$h=4+60 t-16 t^{2}$$ describes the ball's height above the ground, \(h,\) in feet, \(t\) seconds after it was kicked. Use this formula to solve Exercises \(19-20 .\) What was the ball鈥檚 height 2 seconds after it was kicked?
a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$\text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. }$$ How old is the son? b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
Give an example of a rational number that is not an integer.
Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{2 x+y}{x y-2 x}, \text { for } x=-2 \text { and } y=4$$
Explain how to factor the difference of two squares. Provide an example with your explanation.
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