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3 years ago

Put these number in order from least to greatest 6/40 11/20 -7/25 6

Mathematics

1 answer:

egoroff_w [7]3 years ago

4 0

Answer:

-7/25, 6/40, 11/20, 6

Step-by-step explanation:

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What is the sum of 421, 237, 112, and 100?

ipn [44]

Answer:

870

Step-by-step explanation:

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3 years ago

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Which of the following is a solution to the quadratic equation x2-3x-54=0

BaLLatris [955]

Answer:

Step-by-step explanation:

x² - 3x - 54 = 0

x² - 9x + 6x - 54 = 0

x(x - 9) + 6(x - 9) = 0

(x - 9)(x + 6) = 0

x = -6,9

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2 years ago

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Ana has been adding $30 to her saving account every month. Which model could represent the money in Ana’s saving account (y) aft

Gekata [30.6K]

Answer:

y = 30x

Step-by-step explanation:

y is the amount of money

30 is the constant, the amount of money she gets per x, month

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3 years ago

Are the ratios 25/45 and 15/27 proportional? Explain.

liberstina [14]

Write them out as a fraction then reduce them. If theyre the same then its proportional.

25/45 can be cancelled down to 5/9

15/27 can be cancelled down to 3/9

So no theyre not.

6 0

2 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

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:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

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

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

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

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:

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

3 0

3 years ago