Two cylindrical resistors are made of the same material and have the same resistance. The resistors, R1 and R2, have different radii, r1 and r2, and different lengths, L1 and L2. Which of the following relative values for radii and lengths would result in equal resistances?

a. r1 = r2 and L1 = 2L2
b. 2r1 = r2 and L1 = 2L2
c. r1 = r2 and 4L1 = L2
d. 2r1 = r2 and 4L1 = L2

The car hoist allows the car to be driven onto the platform, after which the rear wheels are raised. if the loading from both rear wheels is 1380 lb, determine the force in the hydraulic cylinder ab. neglect the weight of the platform itself. member bcd is a right-angle bell crank pinned to the ramp at c. the force is positive if in tension, negative if in compression.

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 ⇒

Which features on mars point to the possibility of liquid water on the planet? impact craters with sharp rims volcanic cones with craters gullies and stream-like channels mountain ranges with faults