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Leno4ka [110]
3 years ago
9

Please Help... Thanks!

Mathematics
1 answer:
Brut [27]3 years ago
6 0

Answer:

The system of linear inequalities to represent the graph is:

(1) y<=6 and

(2) y>=x

Step-by-step explanation:

The graph is:

1) The region below the horizontal line y=6: y<=6

2) The region above the oblique line that passes through the points:

Origin: O=(0,0)→P1=(0,0)=(x1,y1)→x1=0, y1=0

P2=(5,5)=(x2,y2)→x2=5, y2=5

Slope: m=(y2-y1)/(x2-x1)

m=(5-0)/(5-0)

m=(5)/(5)

m=1

Equation Point-slope:

y-y1=m(x-x1)

y-0=1(x-0)

y=1(x)

y=x

Above the line y=x: y>=x

Then the system of linear inequalities to represent the graph is:

(1) y<=6 and

(2) y>=x



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<h2>4.16%</h2>

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A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and
goldfiish [28.3K]

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and flows out at a rate of

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\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}

e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}

The left side is the derivative of a product:

\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}

Integrate both sides:

e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt

e^{t/800}S(t)=64e^{t/800}+C

S(t)=64+Ce^{-t/800}

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As t\to\infty, the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

7 0
4 years ago
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