consider the limacon with equation r = 3 + 4cos(θ). how does the quotient of a and b relate to the existence…

consider the limacon with equation r = 3 + 4cos(θ). how does the quotient of a and b relate to the existence of an inner loop? because a/b > 1, the curve is a limacon with an inner loop. because b/a > 1, the curve is a limacon with an inner loop. because a/b > 1, the curve is a limacon without an inner loop. because b/a > 1, the curve is a limacon without an inner loop.

consider the limacon with equation r = 3 + 4cos(θ). how does the quotient of a and b relate to the existence of an inner loop? because a/b > 1, the curve is a limacon with an inner loop. because b/a > 1, the curve is a limacon with an inner loop. because a/b > 1, the curve is a limacon without an inner loop. because b/a > 1, the curve is a limacon without an inner loop.

Answer

Explanation:

Step1: Identify a and b in the limacon equation

For the limacon equation $r = a + b\cos(\theta)$, here $a = 3$ and $b = 4$.

Step2: Calculate the quotient $\frac{b}{a}$

$\frac{b}{a}=\frac{4}{3}>1$.

Step3: Recall the condition for inner - loop

For a limacon $r=a + b\cos(\theta)$ (or $r=a + b\sin(\theta)$), if $\frac{b}{a}>1$, the limacon has an inner loop.

Answer:

Because $\frac{b}{a}>1$, the curve is a limacon with an inner loop.