Danielle walked from her house to several locations in her town. The graph represents her distance from home after x hours.
2 answers:
Answer:
<h3>a. How far from home was Danielle after 1/2 hour?</h3>According to the graph, after half hour, Danielle was 1 mile far from home.
<h3>b. What was Danielle's speed between 0 and 1 hour?</h3>To find the speed we have to apply the formula:
From and
, Danielle went from
to
. Replacing this values, we calculate the speed:
Therefore, the speed between 0 and 1 hour is 2 miles per hour.
<h3>c. What was Danielle's speed between 1 and 2 hours?</h3>The Danielle's speed between 1 and 2 hours is zero (). Because, according to the graph, during this time, Danielle didn't move, and without move, there's no speed.
The domain when the function is increasing refers to the increasing <em>x </em>intervals.
From the graph, this increasing interval is from 0 to 1 hours only, it's the only period of time when Danielle was increasing her position.
<h3>e. What is the domain when the function is decreasing?</h3>The parts of the decreasing domain are:
- From 2 to 3 hours.
- From 3 and a half to 4 hours.
In the graph, you can see these decreasing intervals, which are characterized by a downwards direction of the line.
<h3>f. What is the domain when the function is constant?</h3>The parts where the function is constant:
- From 1 to 2 hours.
- From 3 to 3 and a half hours.
Constant intervals, means no increase, no decrease, just an horizontal line.
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It is hard to comprehend your question. As far as I understand:
f(x,y) = e^(-x)
Find the volume over region R = {(x,y): 0<=x<=ln(6), -6<=y <= 6}.
That is all I understood. It would be easier to understand with a picture or some kind of visual aid.
Anyways, to find the volume between the surface and your rectangular region R, we must evaluate a double integral of f on the region R.
Now evaluate,
which evaluates to, 5/6 if I did the math correct. Correct me if I am wrong.
Now integrate this w.r.t. y:
So,