Use ray diagrams to locate the images of the following objects: (a) an object that is 10 cm from a convex lens of +15-cm focal length and (b) an object that is 10 cm from a concave lens of -15-cm focal length. (c) Calculate the image locations for parts (a) and (b) using the thin lens equation. Check for consistency.

Find the first partial derivatives of the function. f(x, y)=x/(x+y)^2

A beam of light passes from air into a transparent petroleum product, cyclohexane, at an incident angle of $48^{\circ}$. The angle of refraction is $31^{\circ}$. What is the index of refraction of the cyclohexane?

Graph: x = 3

A certain wave on a string is found to have a frequency of $500 \mathrm{~Hz}$ and a wavelength of $0.60 \mathrm{~m}$. If a new wave of frequency $250 \mathrm{~Hz}$ is then established on this string and the wave speed does not change, is the new wavelength:

(a) $0.60 \mathrm{~m}$

(b) $0.30 \mathrm{~m}$

(c) $1.2 \mathrm{~m}$

Is smokeless tobacco less harmful than cigarettes? Why or why not?

Write with rational exponents, and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form. $\sqrt[4]{\sqrt[3]{m}}$

A rocket is launched at an angle of $53.0 ^ { \circ }$ above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s$^2$. At this time, its engines fail and the rocket proceeds to move as a projectile. Find its total time of flight.

Choose the word that is closest in meaning to the first word. ominous: (a) threatening, (b) dishonest, (c) dark

A 0.3-L glass of water at 20$^\circ{}$C is to be cooled with ice to 5$^\circ{}$C. Determine how much ice needs to be added to the water, in grams, if the ice is at (a) 0$^\circ{}$C and (b) -20$^\circ{}$C. Also determine how much water would be needed if the cooling is to be done with cold water at 0$^\circ{}$C. The melting temperature and the heat of fusion of ice at atmospheric pressure are 0$^\circ{}$C and 333.7 kJ/kg, respectively, and the density of water is 1 kg/L.

How much heat is required to melt a 2.5-kg block of ice at $0^{\circ} \mathrm{C}?$

Tell whether the data are qualitative or quantitative. Explain your reasoning. shoe sizes of students in your class

Do not compute the Fourier series, but graph the function to which the Fourier series converges, showing at least three full periods.

$$f(x)=\left\{\begin{array}{ll}{2,} & {\text { if }-2<x<-1} \\ {-2,} & {\text { if }-1<x<1} \\ {0,} & {\text { if } 1<x<2}\end{array}\right.$$

Which of these events most expanded democracy, and why?