Q 51. - Calculus

Question

Annie’s second potential design for the central cross section of her kayak is

$r=0.83\left(1-0.5\sin \theta \right)\left(1+0.2{\cos }^2\theta \right)$

Will this design allow Annie to use just two widths of the fabric? (Hint: Use a numerical integration technique to approximate the length of the cross section.)

Step-by-Step Solution

Answer

Yes, the design allows Annie to use just two widths of the fabric 

Step 1. Given information

Annie’s second potential design  is$r=0.83\left(1-0.5\sin \theta \right)\left(1+0.2{\cos }^2\theta \right)$

Step 2. Explanation

Consider the following figure:

Annie’s second potential design for the central cross section of her kayak is $r=0.83\left(1-0.5\sin \theta \right)\left(1+0.2{\cos }^2\theta \right)$

Yes, the design allows Annie to use just two widths of the fabric as there are two loops. One from above x-axis and one below x-axis.