Looking at the unit circle:
tanӨ = tan(Ө <span>± 180k)
If we add/subtract 180° from our angle, it simply ends up on the other side of the unit circle. Since tan</span>Ө is represented as slope, the values of the two are the same.
cotӨ is defined as the reciprocal of tanӨ (1/tanӨ)
If tanӨ = tan(Ө ± 180k), then we could also say that
1/tanӨ = 1/tan(Ө ± 180k) which then becomes cotӨ = cot(Ө ± 180k)
Let's apply this to cot(290°).
Subtract 180° to find that cot(290°) = cot(110°)
cot(110°) = -cot(70°) because the angle has been reflected across the y axis, making its slope opposite.
-cot(70°) = -1/tan(70°) because of that reciprocal property from earlier
tan(70°) ≈ 2.75
-1/tan(70°) ≈ -0.36 = cot(290°)
(of course, most calculators can handle tan(110°), but if you're using a trig chart it might not be on there. include whichever steps are necessary)
The average rate of change is equal to 10 miles per hour.
<h3>What is the average rate of change?</h3>
It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Given that the function is changing from point (30,2) to (20,1). The average rate of the change will be calculated as,
The average rate of change = ( 30 - 20) / ( 2 - 1)
Average rate of change = 10 miles per hour
Therefore, the average rate of change is equal to 10 miles per hour.
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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.
Answer:
$300.25
Step-by-step explanation:
Because $550.75 - $105 - $45.50 - $100 = $300.25
