Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality. Explain
your reasoning.
1 answer:
Answer: The graph does not show two quantities that vary directly, because the line does not pass through the origin.
Step-by-step explanation:
By definition, you know that Direct variation equations have the following form:
Where "k" is the constant of proportionality.
The equation means that when "x" increases, "y" increases" and the ratio does not change.
Now, it is very important to remember the following:
- The graph of a Direct variation equations is a line whose slope is "k".
- The line must passes throug the origin ()
Observe the graph provided.
As you can notice, the line does not pass through the origin; therefore, that graph does not show two quantities that vary directly.
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Answer:
Step-by-step explanation:
Given:
The given AP is.
12,0,-12,......
The first term of an AP
Common difference
We use the the formula for nth term of an AP.
for 87th term
Therefore, The 87th term of given series is -1020.
Look at the attached figure. We define the unit circle as a circle with center in the origin (0,0) and radius 1.
Then, we consider a point P on the circumference. We call the angle between the positive half of the x axis and the radius AP.
We define
As you can see, ACD is a right triangle, and so we have
But since we know that AD is the cosine, AC is the sine, and AP is the radius (which is 1, and remains 1 when squared), we have just found out that
