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If the equation is r = 3 +4cos(θ) then because b/a>1 the curve is a limacon with an inner loop.
Given limacon with equation r=3+4cos(θ) and we have to answer how the quotient of a and b relate to the existence of an inner loop.
Equation is like a relationship between two or more variables expressed in equal to form and it is solved to find the value of variables.
formula of polar graph is similar to r= a+ b cos (θ).
Case 1. If a<b or b/a>1
then the curve is a limacon with inner loop.
Case 2. If a>b or b/a<1
Then the limacon does not have an inner loop.
Here given that (θ)
It is observed that , a<b or b/a>1
Therefore the curve is limacon with an inner loop.
Hence because b/a>1 the curve is a limacon with an inner loop.
Learn more about limacon at brainly.com/question/14322218
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Answer:
Step-by-step explanation:
<u>Given is the geometric series, because the ratio of consecutive terms is common:</u>
The first term is 112.
<u>So the nth term is:</u>
<u>The 9th term is:</u>