CAN SOMEONE PLEASE ANSWER MY LAST QUESTION . WOULD MAKE MY DAY THANKS.
2 answers:
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As the fellow above said, the particle does make a U-turn at the vertex, and we can find that out by getting the derivative of s(t) and zeroing it out to get the point of the horizontal tangent.
Bearing in mind that ds/dt is really v(t) or the velocity equation, so when we zero out the ds/dt, is the same as saying the velocity went to 0, since it got zeroed out, and then the particle goes over the vertex and changes direction.
the negative acceleration value, simply means a decreasing rate of change, so, it means the particle is slowing down and possibly coming to a stop before changing direction again.
Bearing in mind that ds/dt is really v(t) or the velocity equation, so when we zero out the ds/dt, is the same as saying the velocity went to 0, since it got zeroed out, and then the particle goes over the vertex and changes direction.
the negative acceleration value, simply means a decreasing rate of change, so, it means the particle is slowing down and possibly coming to a stop before changing direction again.
Answer:
a) The length of its edge is 8 units.
b) The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.
Step-by-step explanation:
a) The volume of a cube (), measured in cubic units, is defined by the following expression:
(1)
Where is the side length of the cube, measured in units.
If we know that , then the length of its edge is:
The length of its edge is 8 units.
b) The volume of a sphere (), measured in cubic units, that fits snugly inside this cube is defined by:
(2)
If we know that , then the volume of the sphere is:
The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube taken by the sphere is the ratio of the volume of the sphere to the volume of the cube. That is to say:
If we know that and
, then the fraction of the cube that is taken up by the sphere is:
The result in percentage form is calculated by multiplying the result above by 100.
The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.