An island is 1 mi due north of its closest point along a straight shoreline. a visitor is staying at a cabin on the shore that is 15 mi west of that point. the visitor is planning to go from the cabin to the island. suppose the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph. how far should the visitor run before swimming to minimize the time it takes to reach the island? round your answer to three decimal places and omit units from the answer box.

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 ⇒

What is the relationship between the direction of motion of the balloon and the wind currents

What are the necessary conditions for fusion?