The area that is enclosed by the curve defined by the polar equation r = sin θ sin(4θ). can be solved by using the formula of A= ∫[f(θ)]²dθ.
Note also that this all given polar function can be evaluated from a limit 0 to 2 π.
First we sketch the polar curve which is r=sin4θ
Then Derive a Polar Curve where:
r = x² + y²
tan⁻¹
The graph for r=sin4θ is given in the image attached.
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The length of eastern continental trail is 5400 miles and length of erie canal trail is 360 miles.
Step-by-step explanation:
Given,
Combined length of both trails = 5760 miles
Let,
x be the length of eatern continental trail.
y be the length of Erie canal trail.
According to given statement;
x+y=5760 Eqn 1
x = 15y Eqn 2
Putting value of x from Eqn 2 in Eqn 1
Dividing both sides by 16
Putting y=360 in Eqn 2
The length of eastern continental trail is 5400 miles and length of erie canal trail is 360 miles.
Keywords: linear equation, substitution method
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