Identify the curve by finding a cartesian equation for the curve r^2 sin 2 theta=1

The answer is

The transformation between polar and cartesian coordinates is

Now use the trigonometric identity to rewrite the expression as

Now recall the transformations to rewrite

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet