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____ [38]
1 year ago
7

A company's profit is described by the equation P(x)=-5x^2+300x+15,000

Mathematics
2 answers:
qaws [65]1 year ago
4 0

When x=30 units, y = profit = -5(30)^2 + 300(30) + 15000 = $19500

Novay_Z [31]1 year ago
3 0
<span>P(x)=-5x^2+300x+15,000 is the equation of a parabola and represents profit.  Its graph opens down.  Our job is to find the x-coordinate of the vertex (which is the x-coord of the maximum profit) and then the corresponding y-value.

The formula x = -b / (2a) will produce that x-coordinate:

        -(300)
x = ------------ = 30
         2(-5)

When x=30 units, y = profit = -5(30)^2 + 300(30) + 15000 = $19500  (answer)



</span>
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Answer:

The concentration of salt in the tank approaches 35 \mathrm{g} / \mathrm{L},

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Data provide in the question:

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Concentration of salt \lim _{t \rightarrow \infty} C(t)=\lim _{t \rightarrow \infty} \frac{35 t}{320+t}

Now,

Dividing both numerator and denominator by t, we have

\lim _{t \rightarrow \infty} \frac{\frac{1}{t} 35 t}{\frac{1}{t}(320+t)}=\lim _{t \rightarrow \infty} \frac{35}{\frac{320}{t}+1}=35

Here,

The concentration of salt in the tank approaches 35 \mathrm{g} / \mathrm{L},

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