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2 years ago

It’s been a long summer. How do you find a percent of a fraction?

1 answer:

7 0

Do you have a calculator? If so, divide the numerator by the denominator. For example... 2/7: take 2 divided by 7 and you get 28.6%

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Solve the equation ( 32 3) (33) = 36 = X

Allisa [31]

Answer: D. -30

Step-by-step explanation: EDGE 2022 I GOT 100%

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2 years ago

Factor completely.

Svetach [21]

Answer:

in what do u need help?

Step-by-step explanation:

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2 years ago

How many times greater is the population of China than the population of France

jekas [21]

Answer:

China is about 17 times bigger than France.

Meanwhile, the population of France is ~67.1 million people. (1.3 billion more people live in China).

Step-by-step explanation:

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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

2 years ago

Provide the first six terms of the following sequence: t1=81 tn=1/3tn-1

Andrews [41]

We get tne n-th term with: tn=1/3tn-1

We know that the first term is t1=81, so 81=1/3t*1-1

81=1/3t-1

82=1/3t

82*3t=1

3t=1/82

t=1/82*3=1/246

The second term is: 1/

2*(1/246)*2)-1

We get the third term by replacing n with 3 and so on...

8 0

2 years ago

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