The three questions that every economy must answer are: what to produce, how to produce, and whom to produce. Which of the following describes how a mixed command and a mixed market economy would answer those questions A. a mixed command does not answer at all

B. a mixed command economy allows for much more individual freedom in answering the questions

C. a mixed command economy answers the questions based on custom habits

D. a mixed command economy allows for much less individual freedom in answering all the questions

d

Explanation:

Just think of how when someone command you to do something you don't really have a choice in what you do

V = 125π/6 h³

Step-by-step explanation:

First, let's draw a cross section.  If the radius of the sphere is R, and the radius of the cylindrical hole is r, and the height is 5a, then using Pythagorean theorem, we can write:

R² = r² + (5h/2)²

Now let's slice the sphere into concentric shells (like Russian nesting dolls).  Each shell is a hollow cylinder with a radius x, a thickness dx, and a height 2y.  The volume of each shell is:

dV = 2π r h t

dV = 2π (x) (2y) (dx)

dV = 4π x y dx

x² + y² = R², so:

dV = 4π x √(R² − x²) dx

The total volume is the sum of all the shells from x=r to x=R.

V = ∫ dV

V = ∫ 4π x √(R² − x²) dx

If u = R² − x², then du = -2x dx, and -2du = 4x dx.

V = ∫ -2π √u du

V = -2π ∫ √u du

V = -2π (⅔ u^(3/2)) + C

V = -4π/3 u^(3/2) + C

V = -4π/3 (R² − x²)^(3/2) + C

Evaluate from x=r to x=R.

V = -4π/3 (R² − R²)^(3/2) − -4π/3 (R² − r²)^(3/2)

V = 4π/3 (R² − r²)^(3/2)

Since R² = r² + (5h/2)², then R² − r² = (5h/2)².

V = 4π/3 ((5h/2)²)^(3/2)

V = 4π/3 (5h/2)³

V = 125π/6 h³

The volume of both napkin rings is the same, and does not depend on the radius of the sphere or the radius of the hole.