I think you meant to say "scarce" and not "scare". If so, then the answer is D) natural
Anything that is common would be stuff you find everyday and it's everywhere. Scarce is the complete opposite, meaning rare or hard to find. An example would be a rock that is common and gold that is scarce.
Things that are human-made are the complete opposite of natural things such as water, or anything you would find out in nature without human intervention.
This is the concept of quadratic equations, solving the equation 2x^2-12x+20=0 using the formula we get:
x=[-b+/-sqrt(b^2-4ac)]/(2a)
from our equation, a=2,b=-12 and c=20
x=[-(-12+/-sqrt((-12)^2-4*2*20)]/(2*2)
x=[12+/-sqrt(144-160]/4
x=[12+/-sqrt(-16)]/4
x=[12+/-4i]/4
x=[3+\-i]
the answer is A] 3+/-i
To find such critical points, you have to differentiate the function and let the derivative equal zero. Since this function is y written in terms of x, but implicitly, you must use implicit differentiation. Do you know how to do that?
2x^2 - 2x - 40 = 2x^2 -10x + 8x - 40 = 2x(x - 5) + 8(x - 5)
= (x-5)(2x+8) = 2(x-5)(x+4)
