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.
The 2 is in the tenths place so it is two-tenths.
Two-tenths = 2/10= .2
I hope that answers your question.
Answer:
one balloon will be left over
Step-by-step explanation:
Answer:
-1066.65 to 2 decimal places.
Step-by-step explanation:
(−800)+(−200)+(−50)+(−12.5)+...
This is a Geometric series with common ratio r =(-200) / ) / (-800) = 0.25 and first term a1 = -800.
Sum of n terms = a1 * (1 - r^n) / (1 - r)
Sum of 8 terms = -800 * (1 - 0.25^8) / (1 - 0.25)
= -800 * 1.333313
= -1066.65.
