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laila [671]
3 years ago
14

Determine whether the relationship between the circumfrance of a circle and its diameter is a direct variation. If so, identify

the constant of proportionality. Justify your response.
Mathematics
1 answer:
kipiarov [429]3 years ago
3 0

Answer:

The relationship between the circumference of a circle and its diameter represent  a direct variation and the constant of proportionality is equal to the constant \pi

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where K is the constant of proportionality

In this problem we know that

The circumference of a circle is equal to

C=\pi D

therefore

the relationship between the circumference of a circle and its diameter is a direct variation and the constant of proportionality is equal to the constant \pi

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Which of the following describes the graph of 2x + 4y < 16?
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<h3>Answer: A) Dashed line, shaded below</h3>

=============================================================

Explanation:

2x + 4y < 16 solves to y < -0.5x+4 when you isolate y. The inequality sign does not change direction because we divided both sides by a positive value (in this case, 4).

The graph of y < -0.5x+4 will be the same as the graph of 2x+4y < 16

To graph y < -0.5x+4, we graph y = -0.5x+4 which is a straight line that goes through the two points (0,4) and (2, 3). This is the boundary line of the inequality shaded region. The boundary line is a dashed line because we are not including points on the boundary that are part of the solution set. We only include these boundary points if the inequality sign has "or equal to".

We then shade below the dashed boundary line to indicate points below the boundary line. The shading is done downward due to the "less than" sign.

---------------------

Perhaps another method to find what direction we shade is we can try out a point like (0,0). The point cannot be on the boundary line.

Plug those coordinates into either equation. I'll pick the second equation

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0 < -0.5*0+4

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So this is another way to see that the shaded region is below the boundary line.

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