Imagine slicing through a sphere with a plane (sheet of paper). the smaller piece produced is called a spherical cap. its volume is v= πh2(3r−h) /3, where r is the radius of the sphere and h is the thickness of the cap. find dr/dh for a spherical cap with a volume of 5π/ 3 m3. evaluate this derivative when r=2 m and h=1 m. what is the expression for dr /dh? and evaluate this derivative when r= 2m and h = 1m.

What is the point-slope form of the equation for the line with a slope of -2 that passes through (1,4)?

The swimming pool is open when the high temperature is higher than 20∘c. lainey tried to swim on monday and thursday (which was 33 days later). the pool was open on monday, but it was closed on thursday. the high temperature was 30 ∘c on monday, but decreased at a constant rate in the next 33 days. write an inequality to determine the rate of temperature decrease in degrees celsius per day, d, from monday to thursday.

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?