Lead-214 has a half-life of 43.5 seconds. What percent of a sample of this isotope would be left after a time equivalent to 7 half-lives?

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 ⇒

A3030 cmcm wrench is used to loosen a bolt with a force applied 0.30.3 mm from the bolt. it takes 6060 nn to loosen the bolt when the force is applied perpendicular to the wrench. how much force would it take if the force was applied at a 3030 degree angle from perpendicular? a 3030 cmcm wrench is used to loosen a bolt with a force applied 0.30.3 mm from the bolt. it takes 6060 nn to loosen the bolt when the force is applied perpendicular to the wrench. how much force would it take if the force was applied at a 3030 degree angle from perpendicular?

Aboy with a mass 25 kg climbs into a small tree. he sits on a branch that is 2.o m above to the ground. what is his gravitational potential energy above the ground?