Can someone please help me with this
1 answer:
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Answer:
i.e. relation between speed-distance-time is one such situation that can be modeled using graph
Step-by-step explanation:
There are many real world examples that can be modeled using graph. Graphs are represented on co-ordinate planes, so any real world example that can be represented by use of linear equation can be represented onto a graph.
One such example, is speed-distance-time relation. Uniform speed can be represented on a graph as shown in figure.
So, the equation for speed is represented by equation as follows:
So, if we take distance on y axis and time on x axis with points as (distance,time)
(0,0) ==>
(1,2) ==>
(2,2) ==>
the following points 0,0.5,1 will be plotted on graph. Similarly, more values can be plotted by assuming values for distance and time.
Answer:
a)
b)
The values are too small since is positive for both values of
in. I'm speaking of the
values, 2.9 and 3.1.
Step-by-step explanation:
a)
The point-slope of a line is:
where is the slope and
is a point on that line.
We want to find the equation of the tangent line of the curve at the point
on
.
So we know .
To find , we must calculate the derivative of
at
:
.
So the equation of the tangent line to curve at
is:
.
I'm going to solve this for .
Subtract 5 on both sides:
What this means is for values near
is that:
.
Let's evaluate this approximation function for .
Let's evaluate this approximation function for .
b) To determine if these are over approximations or under approximations I will require the second derivative.
If is positive, then it leads to underestimation (since the curve is concave up at that number).
If is negative, then it leads to overestimation (since the curve is concave down at that number).
is positive for
.
is negative for
.
That is, .
So is positive for both values of
which means that the values we found in part (a) are underestimations.