A small ball is attached to one end of a spring that has an unstrained length of 0.215 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 3.76 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch by 0.0132 m. By how much would the spring stretch if it were attached to the ceiling and the ball allowed to hang straight down, motionless?

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

When you push downward on a book at rest on a table, you feel an upward force. does this force depend on friction? defend your answer.

In a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the cornea, whose vertex is 2.60 cm from the retina. what should be the radius of curvature of the cornea such that the image of an object 40.0 cm from the cornea’s vertex is focused on the retina?