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Chapter 5: Problem 30
Find each product. $$\left(7 x^{4} y^{5}\right)\left(-10 x^{7} y^{11}\right)$$
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In Exercises \(79-82,\) simplify each expression. $$\left(\frac{18 x^{2} y^{4}}{9 x y^{2}}\right)-\left(\frac{15 x^{5} y^{6}}{5 x^{4} y^{4}}\right)$$
We have seen that in \(2009,\) the United States government spent more than it had collected in taxes, resulting in a budget deficit of \(\$ 1.35\) trillion. a. Express 1.35 trillion in scientific notation. b. Express the 2009 U.S. population, 307 million, in scientific notation. c. Use your scientific notation answers from parts (a) and (b) to answer this question: If the 2009 budget deficit was evenly divided among every individual in the United States, how much would each citizen have to pay'? Express the answer in scientific and decimal notations.
Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\frac{\left(2^{1} x^{3} y^{-1}\right)^{-2}\left(2 x^{6} y^{4}\right)^{-2}\left(9 x^{3} y^{3}\right)^{0}}{\left(2 x^{4} y^{6}\right)^{2}}$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$534.7=5.347 \times 10^{3}$$
An object that is falling or vertically projected into the air has its height, in feet, above the ground given by $$s=-16 t^{2}+v_{0} t+s_{0}$$ where s is the height, in feet, \(v_{0}\) is the original velocity of the object, in feet per second, \(t\) is the time the object is in motion, in seconds, and \(s_{0}\) is the height, in feet, from which the object is dropped or projected. The figure shows that a ball is thrown straight up from a rooftop at an original velocity of 80 feet per second from a height of 96 feet. The ball misses the rooftop on its way down and eventually strikes the ground. Use the formula and this information to solve Exercises. How high above the ground will the ball be 6 seconds after being thrown? Describe what this means in practical terms.
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