How much heat is needed to raise the temperature of 100g of steel (c= 0.11 kcal/kg 0C) by 15 0C?

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 radius of a sphere is increasing at a rate of 9 cm/ sec. find the radius of the sphere when the volume and the radius of the sphere are increasing at the same numerical rate.

A1500 w electric heater is plugged into the outlet of a 120 v circuit that has a 20 a circuit breaker. you plug an electric hair dryer into the same outlet. the hair dryer has power settings of 600 w, 900 w , 1200 w, and 1500 w. you start with the hair dryer on the 600 w setting and increase the power setting until the circuit breaker trips. under what setting does the circuit breaker trip.