Asphere of radius 3 inches is sliced with two parallel planes: one passes through the equator and the other is h inches above the first plane. the resulting portion of the sphere between the two planes is called a spherical segment; see the picture: in math 125, you will show that the volume v of the spherical segment is given by this formula (which we will assume): v = (π/3)h(27 – h2). give exact answers to the questions below. (a) find the volume of the spherical segment if h=1: (b) find the rate of change of the volume with respect to h of the spherical segment at h=1: (c) use the tangent line approximation at h=1 to estimate the value of h that will yield a spherical segment having volume 25 cubic inches:

V = (π/3)H(27 – H2) : Please see attachment

a. Volume =26π/3

b.rate of change of the volume with respect to H = 8π

c.H=0.0114 inch

Step-by-step explanation:

Please see attachment

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

b

step-by-step explanation:

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