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natulia [17]
2 years ago
14

Find the value of n in this equation.

Mathematics
1 answer:
lisabon 2012 [21]2 years ago
3 0

Answer:

  • D. 9

=========================

<h2>Given </h2>

Triangle with:

  • Base of n² -3,
  • Midsegment of 39.

<h2>To find</h2>

  • The value of n.

<h2>Solution</h2>

As per definition of midsegment, it is connecting the midpoints of two sides and its length is half the length of the opposite side of the triangle.

So we have:

  • (n² - 3)/2 = 39

Solve it for n:

  • n² - 3 = 78
  • n² = 81
  • n = √81
  • n = 9

Correct choice is D.

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A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain
MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

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\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}

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\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C

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(iv) Solve for A as a function of time.

\text{The integrated rate expression is}\\\ln A = -0.003t +  \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

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b.Calculate the concentration

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\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

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