Elena was pouring coffee at a constant rate into a mug similar to the one shown in the figure. Counting the seconds to fill the mug with coffee, Elena calculated that she is pouring coffee at 25ml/sec. The mug has a height of 10 cm and it took Elena about 5 seconds to fill the mug to the brim. Sketch a graph of the depth of the coffee in the mug as a function of time. Account for the shape of the graph in terms of concavity. By looking at your graph, describe how the depth of the coffee in the mug is changing and answer the following: a) At first, the depth of the coffee in the mug is changing at a (Key words for your description: rate, faster, slower). I know that, because Then, the depth of the coffee is increasing at a b) Around second the mug is filling at the fastest rate. I estimate that, at that time, the depth of the coffee would be about cm. C) The inflection point of the function would be The inflection point is the point where d) The average rate of change of the depth of the coffee is about (use units of measure). Around second and second (fill in the values in ascending order), the rate of change of the depth is the same as the average rate of change.
Elena was pouring coffee at a constant rate into a mug similar to the one shown in the figure. Counting the seconds to fill the mug with coffee, Elena calculated that she is pouring coffee at 25ml/sec. The mug has a height of 10 cm and it took Elena about 5 seconds to fill the mug to the brim. Sketch a graph of the depth of the coffee in the mug as a function of time. Account for the shape of the graph in terms of concavity. By looking at your graph, describe how the depth of the coffee in the mug is changing and answer the following: a) At first, the depth of the coffee in the mug is changing at a (Key words for your description: rate, faster, slower). I know that, because Then, the depth of the coffee is increasing at a b) Around second the mug is filling at the fastest rate. I estimate that, at that time, the depth of the coffee would be about cm. C) The inflection point of the function would be The inflection point is the point where d) The average rate of change of the depth of the coffee is about (use units of measure). Around second and second (fill in the values in ascending order), the rate of change of the depth is the same as the average rate of change.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Elena was pouring coffee at a constant rate into a mug similar to the one shown in the figure. Counting the seconds to fill
the mug with coffee, Elena calculated that she is pouring coffee at 25ml/sec. The mug has a height of 10 cm and it
took Elena about 5 seconds to fill the mug to the brim.
Sketch a graph of the depth of the coffee in the mug as a function of time. Account for the shape of the graph in terms
of concavity. By looking at your graph, describe how the depth of the coffee in the mug is changing and answer the
following:
a) At first, the depth of the coffee in the mug is changing at a
(Key words for your description: rate, faster, slower). I
know that, because
Then, the depth of the coffee is increasing at a
b) Around second
the mug is filling at the fastest rate. I estimate that, at that time, the depth of the coffee would be about
cm.
C) The inflection point of the function would be
The inflection point is the point where
d) The average rate of change of the depth of the coffee is about
(use units of measure). Around second
and
second
(fill in the values in ascending order), the rate of change of the depth is the same as the average rate of change.
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