Tutored student athletes at Cornell as a part of the "Big Red Tutoring" team. I specifically tutored an introductory Linear Algebra, and Differential Equations class.
Sensitive Eyes. After an eye examination, you put some eyedrops on your sensitive eyes. The cornea (the front part of the eye) has an index of refraction of $1.38,$ while the eyedrops have a refractive index of $1.45 .$ After you put in the drops, your friends notice that your eyes look red, because red light of wavelength 600 nm has been reinforced in the reflected light. (a) What is the minimum thickness of the film of eyedrops on your cornea? (b) Will any other wavelengths of visible light be reinforced in the reflected light? Will any be cancelled? (c) Suppose you had contact lenses, so that the eyedrops went on them instead of on your corneas. If the refractive index of the lens material is 1.50 and the layer of eyedrops has the same thickness as in part (a), what wavelengths of visible light will be reinforced? What wavelengths will be cancelled?
In what is the ratio of the sun's gravitational force on you to the earth's gravitational force on you?
The centers of a $10 \mathrm{kg}$ lead ball and a $100 \mathrm{g}$ lead ball are separaied by $10 \mathrm{cm} .$a. What gravitational force does each exert on the other?b. What is the ratio of this gravitational force to the gravitational force of the earth on the $100 \mathrm{g}$ ball?
What is the ratio of the sun's gravitational force on the moon to the earth's gravitational force on the moon?
A 1.0 -m-diameter lead sphere has a mass of 5900 kg. A dust particle rests on the surface. What is the ratio of the gravitational force of the sphere on the dust particle to the gravitational force of the earth on the dust particle?
Estimate the force of attraction between a $50 \mathrm{kg}$ woman and a $70 \mathrm{kg}$ man siting $1.0 \mathrm{m}$ apart.
A crew rows 36 kilometers in 2 hours with the current, and thesame distance in 3hours against the current. What is their speed in still water(in kph)?
Graph each inequality. Do not use a calculator. $$4 y-3 x<5$$
Find the eigenvalues and eigenfunctions for the given boundary-value problem.$$y^{\prime \prime}+\lambda y=0, \quad y^{\prime}(0)=0, \quad y^{\prime}(\pi)=0$$
The Monkey at the Typewriter Suppose that a monkey is seated at a computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 24 characters (including spaces) will be "beware the ides of march". (Leave your answer as a formula.)
Investments Compute the specified quantity.A corporate bond paying $4,000 after 12 weeks earns 0.03% simple interest per week. How much did it cost to buy? (Round your answer to the nearest cent.)
