A regular polygon has about 5 lines of symmetry. The number of lines of symmetry is equivalent to the number of sides.
Answer:
Correct integral, third graph
Step-by-step explanation:
Assuming that your answer was 'tan³(θ)/3 + C,' you have the right integral. We would have to solve for the integral using u-substitution. Let's start.
Given : ∫ tan²(θ)sec²(θ)dθ
Applying u-substitution : u = tan(θ),
=> ∫ u²du
Apply the power rule ' ∫ xᵃdx = x^(a+1)/a+1 ' : u^(2+1)/ 2+1
Substitute back u = tan(θ) : tan^2+1(θ)/2+1
Simplify : 1/3tan³(θ)
Hence the integral ' ∫ tan²(θ)sec²(θ)dθ ' = ' 1/3tan³(θ). ' Your solution was rewritten in a different format, but it was the same answer. Now let's move on to the graphing portion. The attachment represents F(θ). f(θ) is an upward facing parabola, so your graph will be the third one.
The graph is not a direct variation because the line does not go through the origin; option C.
<h3>What is a direct variation?</h3>
A direct variation is a relationship between two or more quantities in which as one quantity increases, the other quantity also increases. Similarly, if the other quantity decreases, the other decreases as well.
For the graph of a direct variation, the line must pass through the origin.
Therefore, the graph does not represent a direct variation because the line does not go through the origin.
In conclusion, direct variation involves a corresponding increase or decrease in two related quantities.
Learn more about direct variation at: brainly.com/question/2633726
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