What is the sign of the trigonometric function, given the quadrant the terminal ray of an angle lies in? Select all correct statements.

The sine function is positive in quadrant I .

The cosecant function is positive in quadrant IV .

The cotangent function is negative in quadrant II .

The cosine function is negative in quadrant II .

The secant function is positive in quadrant III .

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Ответ:

KaliBratz

20.03.2023

Mathematics

Salt flows into the tank at a rate of

(1/2 lb/gal) * (6 gal/min) = 3 lb/min

and flows out at a rate of

(Q(t)/60 lb/gal) * (6 gal/min) = 6Q(t) lb/min

The net rate of change of the amount of salt in the tank at time is then governed by

$\dfrac{\mathrm dQ}{\mathrm dt}=3-6Q$

Solve for :

$\dfrac{\mathrm dQ}{\mathrm dt}+6Q=3$

$e^{6t}\dfrac{\mathrm dQ}{\mathrm dt}+6e^{6t}Q=3e^{6t}$

$\dfrac{\mathrm d}{\mathrm dt}[e^{6t}Q]=3e^{6t}$

$e^{6t}Q=\dfrac{e^{6t}}2+C$

$\implies Q=\dfrac12+Ce^{-6t}$

The tank starts with 10 lb of salt, so that Q(0) = 10. This gives us

$10=\dfrac12+C\implies C=\dfrac{19}2$

so that the amount of salt in the tank at time is given by

$\boxed{Q(t)=\dfrac{1+19e^{-6t}}2}$

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