Imagine slicing through a sphere with a plane (sheet ofpaper). 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.

Demonstrate the proof of your new polynomial identity through an algebraic proof and a numerical proof in an engaging way! make it so the whole world wants to purchase your polynomial identity and can't imagine living without it! you must: label and display your new polynomial identity prove that it is true through an algebraic proof, identifying each step demonstrate that your polynomial identity works on numerical relationships create your own using the columns below. see what happens when different binomials or trinomials are combined. square one factor from column a and add it to one factor from column b to develop your own identity. column a column b (x − y) (x2 + 2xy + y2) (x + y) (x2 − 2xy + y2) (y + x) (ax + b) (y − x) (cy + d)

In the diagram, the ratio of ab to ae is (1/2) . what is the ratio of the length of to the length of ?

Proceed as in example 3 in section 6.1 to rewrite the given expression using a single power series whose general term involves xk. ∞ n(n − 1)cnxn − 2 n = 2 − 4 ∞ ncnxn n = 1 + ∞ cnxn n = 0