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prohojiy [21]
3 years ago
11

The red dot on the number line below represents the square root of an integer. Explain how to determine this integer, and then f

ind it. The red dot is located between 12 and 13. The red dot is about half way between 12 and 13, but a little below the half way point, so the red dot represents a little below half way between the two square roots. Since the square root of 144 is equal to 12 and the square root of 169 is equal to 13, then the red dot is located between the two square roots. By extension, to the nearest integer, the approximate value of the dot will be a little below half way between and , which is about the square root of .
Mathematics
2 answers:
Vesna [10]3 years ago
5 0
It looks like the dot would be placed on about 12.4 or 12.45. I hope that this helped. And that means that the square root would be located at 153.76 or 155.0025. 
motikmotik3 years ago
5 0

Answer: "the square root of" 144 "is equal the 12 and the square root of" 169 "is equal to 13"

"by extension, to the nearest integer, the approximate value of the dark will be a little below half way between square root 144 and square root 169, which is about the square root of" 156

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Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}

By expanding the previous equation:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

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Since there is no accumulation within the tank, expression is simplified to this:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}

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The solution of this equation is:

c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})

The salt concentration after 8 minutes is:

c(8) = 0.166 \frac{pounds}{gallon}

The instantaneous amount of salt in the tank is:

m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds

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