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Magazine Problem 110
The windchill factor is a measure of the cooling effect that the wind has on a person's skin. It calculates the equivalent cooling temperature if there were no wind. The National Weather Service uses the formula $$ \text { Windchill temperature }=35.74+0.6215 T-35.75 V^{4 / 25}+0.4275 T V^{4 / 25} $$ where T is the temperature in \(^{\circ} \mathrm{F}\) and \(\mathrm{Vi}\) is the wind speed in miles per hour, to calculate wind- chill. The table gives the windchill factor for various wind speeds and temperatures at which frostbite is a risk, and how quickly it may occur. Use the formula to determine the windchill temperature to the nearest tenth of a degree, given the following conditions. Compare answers with the appropriate entries in the table. \(10^{\circ} \mathrm{F}, 30-\mathrm{mph}\) wind
Problem 111
Rationalize each denominator. Assume that all radicals represent real numbers and that no denominators are .0 $$ \frac{p}{\sqrt{p+2}} $$
Problem 111
The windchill factor is a measure of the cooling effect that the wind has on a person's skin. It calculates the equivalent cooling temperature if there were no wind. The National Weather Service uses the formula $$ \text { Windchill temperature }=35.74+0.6215 T-35.75 V^{4 / 25}+0.4275 T V^{4 / 25} $$ where T is the temperature in \(^{\circ} \mathrm{F}\) and \(\mathrm{Vi}\) is the wind speed in miles per hour, to calculate wind- chill. The table gives the windchill factor for various wind speeds and temperatures at which frostbite is a risk, and how quickly it may occur. Use the formula to determine the windchill temperature to the nearest tenth of a degree, given the following conditions. Compare answers with the appropriate entries in the table. \(20^{\circ} \mathrm{F}, 20-\mathrm{mph}\) wind
Problem 111
Simplify. Assume that all variables represent positive real numbers. \(\sqrt[3]{4} \cdot \sqrt{3}\)
Problem 112
Simplify. Assume that all variables represent positive real numbers. \(\sqrt[3]{5} \cdot \sqrt{6}\)
Problem 112
Rationalize each denominator. Assume that all radicals represent real numbers and that no denominators are .0 $$ \frac{q}{\sqrt{5+q}} $$
Problem 112
The windchill factor is a measure of the cooling effect that the wind has on a person's skin. It calculates the equivalent cooling temperature if there were no wind. The National Weather Service uses the formula $$ \text { Windchill temperature }=35.74+0.6215 T-35.75 V^{4 / 25}+0.4275 T V^{4 / 25} $$ where T is the temperature in \(^{\circ} \mathrm{F}\) and \(\mathrm{Vi}\) is the wind speed in miles per hour, to calculate wind- chill. The table gives the windchill factor for various wind speeds and temperatures at which frostbite is a risk, and how quickly it may occur. Use the formula to determine the windchill temperature to the nearest tenth of a degree, given the following conditions. Compare answers with the appropriate entries in the table. \(40^{\circ} \mathrm{F}, 10\) -mph wind
Problem 113
Simplify. Assume that all variables represent positive real numbers. \(\sqrt[4]{3} \cdot \sqrt[3]{4}\)
Problem 114
Solve each problem. The following expression occurs in a standard problem in trigonometry. $$\frac{\sqrt{3}+1}{1-\sqrt{3}}$$ Show that it simplifies to \(-2-\sqrt{3}\). Then verify, using a calculator approximation.
Problem 114
Simplify. Assume that all variables represent positive real numbers. \(\sqrt[3]{2} \cdot \sqrt[5]{3}\)
