Let ${ \vec { F } } = 2 x \vec { i } + z \vec { j } + ( y + 2 x ) \vec { k }$

question 44

Short Answer

Let ${ \vec { F } } = 2 x \vec { i } + z \vec { j } + ( y + 2 x ) \vec { k }$ Use Stokes' Theorem to find $\dot { \mathrm { Q } } { \vec { F } \times \vec { d r } }$ where C is a circle in the xy-plane of radius $4$ , centered at $( 3,1,0 )$ oriented counter-clockwise when viewed from above.

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Definitions:

Square Root

The square root of a number is a value that, when multiplied by itself, gives the original number.

P < 0.05

A statistical threshold indicating that the observed results are significant with a probability of less than 5% being due to chance.

Obtained Value

The actual value measured or computed from a data set or experiment, often compared against a theoretic or critical value in hypothesis testing.

Population Standard Deviation

The population standard deviation is a measure of the dispersion or spread of a set of values within a population, quantifying how much the values differ from the population mean.