Chapter 10

Find and correct the error. \(\frac{\sqrt[3]{64}}{\sqrt{64}}=\sqrt[3]{\frac{64}{64}}=\sqrt[3]{1}=1\)

Find and correct the error. See the Concept Check in this section. $$ \frac{\sqrt[3]{64}}{\sqrt{64}}=\sqrt[3]{\frac{64}{64}}=\sqrt[3]{1}=1 $$

Do not use a calculator. \(\sqrt{1000}\) is closest to a. 10 b. 30 c. 100 d. 500

In electronics, the angular frequency of oscillations in a certain type of circuit is given by the expression \((L C)^{-1 / 2} .\) Use radical notation to write this expression.

Find and correct the error. \(\frac{\sqrt[4]{16}}{\sqrt{4}}=\sqrt[4]{\frac{16}{4}}=\sqrt[4]{4}\)

The formula for the radius \(r\) of a sphere with surface area \(A\) is given by \(r=\sqrt{\frac{A}{4 \pi}}\). Calculate the radius of a standard zorb whose outside surface area is 32.17 sq \(m\). Round to the nearest tenth. (A zorb is a large inflated ball within a ball in which a person, strapped inside, may choose to roll down a hill. Source: Zorb, Ltd.)

Before Mount Vesuvius, a volcano in Italy, erupted violently in 79 a.D., its height was 4190 feet. Vesuvius was roughly cone shaped, and its base had a radius of approximately 25,200 feet. Use the formula \(A=\pi r \sqrt{r^{2}+h^{2}}\) for the lateral surface area \(A\) of a cone with radius \(r\) and height \(h\) to approximate the surface area of this volcano before it erupted.

The Mosteller formula for calculating adult body surface area is \(B=\sqrt{\frac{h w}{3131}},\) where \(B\) is an individual's body surface area in square meters, \(h\) is the individual's height in inches, and \(w\) is the individual's weight in pounds. Use this information to answer Exercises 111 and 112. Round answers to 2 decimal places. Find the body surface area of an individual who is 66 inches tall and who weighs 135 pounds.

The owner of Knightime Classic Movie Rentals has determined that the demand equation for renting older released DVDs is \(F(x)=0.6 \sqrt{49-x^{2}},\) where \(x\) is the price in dollars per two-day rental and \(F(x)\) is the number of times the DVD is demanded per week. a. Approximate to one decimal place the demand per week of an older released DVD if the rental price is $$\$ 3$$ per two-day rental. b. Approximate to one decimal place the demand per week of an older released DVD if the rental price is $$\$ 5$$ per two-day rental. c. Explain how the owner of the store can use this equation to predict the number of copies of each DVD that should be in stock.

The Mosteller formula for calculating adult body surface area is \(B=\sqrt{\frac{h w}{3131}},\) where \(B\) is an individual's body surface area in square meters, \(h\) is the individual's height in inches, and \(w\) is the individual's weight in pounds. Use this information to answer Exercises 111 and 112. Round answers to 2 decimal places. Find the body surface area of an individual who is 74 inches tall and who weighs 225 pounds.

Escape velocity is the minimum speed that an object must reach to escape a planet's pull of gravity. Escape velocity \(v\) is given by the equation \(v=\sqrt{\frac{2 G m}{r}},\) where \(m\) is the mass of the planet, \(r\) is its radius, and \(G\) is the universal gravitational constant, which has a value of \(G=6.67 \times 10^{-11} \mathrm{~m}^{3} / \mathrm{kg} \cdot \mathrm{s}^{2} .\) The mass of Earth is \(5.97 \times 10^{24} \mathrm{~kg},\) and its radius is \(6.37 \times 10^{6} \mathrm{~m}\). Use this information to find the escape velocity for Earth in meters per second. Round to the nearest whole number. (Source: National Space Science Data Center)

Suppose a classmate tells you that \(\sqrt{13} \approx 5.7\). Without a calculator, how can you convince your classmate that he or she must have made an error?

Suppose a classmate tells you that \(\sqrt[3]{10} \approx 3.2\). Without a calculator, how can you convince your friend that he or she must have made an error?