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4 years ago

Determine whether the graph is the graph of a function.

Mathematics

2 answers:

photoshop1234 [79]4 years ago

8 0

Answer:

Yes

Step-by-step explanation:

Unless the line is vertical, the graph of any straight line is the graph of a function.

___

A vertical line does not map x to one single y-value, so it does not represent a function. Any other line does map each x to a single y-value, so does represent a function.

Arada [10]4 years ago

5 0

<h2>Answer:</h2>

Yes, the graph is the graph of a function.

<h2>Step-by-step explanation:</h2>

<u>Function--</u>

A function is a collection of all the ordered pair such that each element of the first set is mapped to a single element of the other set.

i.e. each element has a single image.

i.e. no elements of the first set is mapped to more than one element.

Also, the graph of the function passes the vertical line test.

i.e. any line passing through the domain and parallel to the y-axis should intersect the graph at least once.

Hence, from the graph we observe that the graph passes the vertical line test.

Hence, the graph is a graph of a function.

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Answer:

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Step-by-step explanation:

To evaluate f(- 6) , substitute x = - 6 into f(x)

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3 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

Given the box plot, will the mean or the median provide a better description of the center?

yuradex [85]

Answer:

The median, because the data distribution is skewed to the right

Step-by-step explanation:

If the longer part of the box is to the right (or above) the median, the data is said to be skewed right. If the longer part is to the left (or below) the median, the data is skewed left. The data is skewed right. The median would be a better estimate, because one or two numbers on the high end will cause the numbers to be skewed to the right, and the mean to be high

4 0

3 years ago

Read 2 more answers