Each of the following objects is immediately dunked in an identical tub of cold water. the tubs are quickly sealed and insulated.
rank the objects on the basis of their temperature on reaching equilibrium with the water rank from largest to smallest.

wooden cutting board c = 1700 j/(kg·°c) k 0.1 j/(s-m·°c)
well done steak c 3500 j/(kg-° c) k = 0.2 j/(s-m-°c)
aluminum pot c = 900 j/(kg·° c) k 220 j/(s-m-°c)
iron skillet c = 448 j/(kg·°c) k-80 j/(s-m-°c)
glass casserole dish c = 837 j/ (kg·°c) k = 0.8 j/(s·m·°c)
silver ingot c = 235 j/(kg·°c) k-420 j/(s-m .°c)

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

The temperature at a point (x, y) is t(x, y), measured in degrees celsius. a bug crawls so that its position after t seconds is given by x = 6 + t , y = 8 + 1 3 t, where x and y are measured in centimeters. the temperature function satisfies tx(3, 9) = 5 and ty(3, 9) = 4. how fast is the temperature rising on the bug's path after 3 seconds? (round your answer to two decimal places.)

Aperson walks first at a constant speed of 4.89 m/s along a straight line from point a to point b and then back along the line from b to a at a constant speed of 2.95 m/s. what is the average speed over the entire trip?