You can use any angular measure---radians, degrees, or revolutions---in some of the equations in Chapter 999, but you can use only radian measure in others. Identify those for which using radians is necessary and those for which it is not, and in each case give your reasoning.
Find the general solution of following differential equation. Use C,C1,C2,…C, C_1, C_2, \ldotsC,C1,C2,… to denote arbitrary constants.
y′(x)=4tan2x−3cosxy^{\prime}(x)=4 \tan 2 x-3 \cos x y′(x)=4tan2x−3cosx
Windows that look into bathrooms are often translucent instead of transparent. Why?
JWater is being boiled in an open kettle that has a 0.5000.5000.500-cm-thick circular aluminum bottom with a radius of 12.0 cm12.0 \mathrm{~cm}12.0 cm. If the water boils away at a rate of 0.500 kg/min0.500 \mathrm{~kg} / \mathrm{min}0.500 kg/min, what is the temperature of the lower surface of the bottom of the kettle? Assume that the top surface of the bottom of the kettle is at 100∘C100^{\circ} \mathrm{C}100∘C.