You are investigating whether the thickness of a sponge is affected by the amount of mass placed on top of it. What is the dependent variable in this investigation?

Which changes of state do the labels represent? a: b: 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 ⇒

Arunner is jogging at a steady 3.6 km/hr. when the runner is 2.9 km from the finish line, a bird begins flying from the runner to the finish line at 14.4 km/hr (4 times as fast as the runner). when the bird reaches the finish line, it turns around and flies back to the runner. even though the bird is a dodo, we will assume that it occupies only one point in space, i. e., a zero-length bird. how far does the bird travel? (b) after this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. the bird repeats the back and forth trips until the runner reaches the finish line. how far does the bird travel from the beginning? (i. e. include the distance traveled to the first encounter)