Answer:
and 
Step-by-step explanation:
24 kernels in 10 minutes
In 1 minute she can eat 
let 
be the number of popcorn and minutes so the rate of eating popcorn is of the form
So, when 
we get
can be any real number
Other two ratios can be and .
So for this, we will be simplifying √180 and √125 using the product rule of radicals (√ab = √a * √b)
Starting with √180: 
Now with √125: 
Now that we have our simplified radicals, our equation looks like this: 6√5 - 5√5 + √5 . Combine everything, and your answer will be 2√5.
Do you want a general solution or from 0 <= x < 2pi?
tan^2(2x) - 1 = 0
tan^2(2x) = 1
Take the square root of both sides,
tan(2x) = +/- 1
Two equations:
tan(2x) = 1
tan(2x) = -1
Solve each equation.
tan(2x) = 1, 2x = {pi/4, 5pi/4, 9pi/4, 13pi/4},
x = { pi/8, 5pi/8, 9pi/8, 13pi/8 }
tan(2x) = -1, 2x = { 3pi/4, 7pi/4, 11pi/4, 15pi/4 },
x = { 3pi/8, 7pi/8, 11pi/8, 15pi/8}
So for solutions within [0, 2pi),
x = {pi/8, 3pi/8, 5pi/8, 7pi/8, 9pi/8, 11pi/8, 13pi/8, 15pi/8 }
She is paying $0.6 for one pound of dried food. Hope it help!
The answer is gonna be 9 with a remainder or .06 if i’m wrong sorry lowkey kinda dumb ngl:)
