The curvature of the helix r(t)=(acost)i+(asint)j+(bt)k (a, b is greater than or equal to 0) is k=a/(a^2+b^2). what is the largest value k can have for a given value of b?

Consider a function of , keeping fixed:

Differentiate with respect to :

The denominator is always positive except in the case of , so the numerator determines where has its critical points. We have

When , we get a maximum curvature of

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.