Let $\vec { F }$ Be a Smooth Velocity Vector Field Describing the Flow of Field

question 38

Short Answer

Let $\vec { F }$ be a smooth velocity vector field describing the flow of a fluid.Suppose that $\operatorname { div } \vec { F } ( 1,2 , - 1 ) = - 4$ Estimate the value of $\int _ { S }{ \vec { F } } \cdot \vec{ d A }$ where S is a sphere of radius 0.25 centered at (1, 2,-1)oriented outward.Give your answer to 4 decimal places.

---

Definitions:

List Price

The advertised price of a product or service before any discounts or promotions are applied.

New Car Dealer

A business that specializes in selling new automobiles, often featuring a specific brand or range of vehicle models.

Allowances

Funds or discounts given for a particular purpose, such as a price reduction to a retailer from a manufacturer, or money given to children by their parents.

List Price Deductions

Discounts, allowances, or reductions from a product's standard list price that sellers may offer to buyers.