Answer:
3.7 m/s^2
Explanation:
The period of a simple pendulum is given by:

where L is the length of the pendulum and g is the free-fall acceleration on the planet.
Calling L the length of the pendulum, we know that:
is the period of the pendulum on Earth, and
is the free-fall acceleration on Earth
is the period of the pendulum on Mars, and
is the free-fall acceleration on Mars
Dividing the two expressions we get

And re-arranging it we can find the value of the free-fall acceleration on Mars:

A microwaveable cup-of-soup package needs to be constructed in the shape of a cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production costs.
h: height of the cylinder, r: radius of the cylinder
The volume of a cylinder: V=πr2h
Area of the sides: A=2πrh
Area of the top/bottom: A=πr2
The cost of packaging, C=2πrh*0.02+ πr^2*0.02+ πr^2*0.05 subject to the constraint πr^2h=600
C=πr(0.04h+.07r) and the constraint implies h=600/ πr^2
So C=πr(24/πr^2+.07r)=24/r+.07πr^2
C'=-24/r^2+0.14πr=0
r^3=24/0.14π r=3.79 cm
h=600/πr^2=13.3 cm
C=π*3.79*(0.04*13.3+.07*3.79)=9.48cents
C''=0.14π+48/r^3>0 for all r>=0 so our solution is indeed a minimum.
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Answer:
d. All of the above (This is write answer)