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<h3>Answer: 40</h3>
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Explanation:
JQ is longer than QN. We can see this visually, but the rule for something like this is the segment from the vertex to the centroid is longer compared to the segment that spans from the centroid to the midpoint.
See the diagram below.
The ratio of these two lengths is 2:1, meaning that JQ is twice as long compared to QN. This is one property of the segments that form when we construct the centroid (recall that the centroid is the intersection of the medians)
We know that JN = 60
Let x = JQ and y = QN
The ratio of x to y is x/y and this is 2/1
x/y = 2/1
1*x = y*2
x = 2y
Now use the segment addition postulate
JQ + QN = JN
x + y = 60
2y + y = 60
3y = 60
y = 60/3
y = 20
QN = 20
JQ = 2*y = 2*QN = 2*20 = 40
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We have
JQ = 40 and QN = 20
We see that JQ is twice as larger as QN and that JQ + QN is equal to 60.
Answer:
The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.
Step-by-step explanation:
Geometrically speaking, the volume of the right circular cone (), in cubic inches, is defined by the following formula:
(1)
Where:
- Radius, in inches.
- Height, in inches.
Then, we derive an expression for the rate of change of the volume (), in cubic inches per second, by derivatives:
(2)
Where:
- Rate of change of the radius, in inches per second.
- Rate of change of the height, in inches per second.
If we know that ,
,
and
, then the rate of change of the volume is:
The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.