Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

question 78

Short Answer

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , that is, find the flux of $\mathbf { F }$ across $S$ .
$\mathbf { F } ( x , y , z ) = - 4 z \mathbf { i } + y \mathbf { j } - 3 x \mathbf { k } ; \mathrm { S }$ is the hemisphere $z = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } } ; \mathbf { n }$ points upward

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Interest

The charge for borrowing money or the return on invested capital, generally expressed as a percentage rate.

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Movable objects intended to support various human activities such as seating, eating, and sleeping, as well as to hold objects or store items.

Mortgage

A loan specifically used to purchase real estate, where the property serves as collateral until the debt is fully repaid.

Interest Rate

The proportion of a loan that is charged as interest to the borrower, typically expressed as an annual percentage.