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3 years ago

The set of order pairs (-1, 8), (0,3) (1,2) and (2, -7) represent a function. What is the range of the function?

1 answer:

8 0

Answer: The range is the set {8, 3, 2, -7} which can be sorted to get {-7, 2, 3, 8}

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Explanation:

The range is simply the set of possible y values. All you have to do is list all the y coordinates and surround the values in curly braces. The curly braces indicate a set. Every point is of the form (x,y). The y coordinate is the second value listed of each ordered pair.

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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

................... 8x-0.2=9.8

mario62 [17]

Answer:

I love algebra anyways

The ans is in the picture with the steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

1) 5x + 3 = 23<br> Is the value of x 4

Nataly [62]

Answer:

X = 4

Step-by-step explanation:

5x + 3 = 23

Subtract 3 from both sides: 5x = 20

Divide both sides by 5: x = 4

3 0

2 years ago

Gap sells jeans that cost $21.00 for a selling price of $29.95. The percent of markup based on cost is

9966 [12]

If Gap sells jeans that cost $21.00 for selling price of $29.95. The percent of markup based on cost is approximately 43%. The markup in price is exactly $8.95.

3 0

3 years ago

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PLEASE HELP A GIRL OUT!!! What is the best estimate for the value of the expression?

Ivenika [448]

Answer: -2(1/2)

Step-by-step explanation:

I CAN HELP A GIRL OUT!

anyways...

calculate the difference first.

(-13/12) - 14/9

then, rewrite the expression.

-13/12 - 14/9

the solution is -95/36.

when it's converted to decimal form, it turns into -2.638. so, our BEST estimate for the value of the expression is -2(1/2) (the second option)

5 0

2 years ago