Answer:
Air is a mixture.
Explanation:
Air is a homogeneous mixture. It is made up of gaseous substances such as nitrogen, oxygen, and smaller amounts of others.
Carbon dioxide is a pure substance, not a mixture.
Carbon is another pure substance, it cannot be separated into other substances.
Oxygen is just oxygen, it does not contain any other substance.
Answer:

Explanation:
The relationship between angular acceleration α and torque τ is given by :

Here,
is the moment of inertia. It depends on the mass and the distance from the axis of rotation.
is the angular acceleration
Hence, this is the required solution.
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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There are four (4) different colors of socks in his sack.
So, even if he's in a dark room and does it all without looking,
he will absolutely positively definitely have at least 1 matching
pair in has hand after he pulls out 5 socks.
The first 4 could have all been different colors. But the 5th sock
MUST match one of the other four.
Answer:
Please refer to the figure.
q1 is a negative charge, and q2 and q3 are positive charges. So, the force exerted by q1 on q3 is attractive, and the force exerted by q2 on q3 is repulsive, which means F13 is directed towards left, and F23 is also directed towards left.


The net force on q3 is the sum of these two forces:

Since both forces are directed towards left, their sign should be negative.