Use the information about budgets on page 352 to explain how inequalities are used in finances. Include an explanation of the re
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Answer:
The maximum acceleration over that interval is .
Step-by-step explanation:
The acceleration of this car is modelled as a function of the variable .
Notice that the interval of interest is closed on both ends. In other words, this interval includes both endpoints:
and
. Over this interval, the value of
might be maximized when
is at the following:
- One of the two endpoints of this interval, where
or
.
- A local maximum of
, where
(first derivative of
is zero) and
(second derivative of
is smaller than zero.)
Start by calculating the value of at the two endpoints:
.
.
Apply the power rule to find the first and second derivatives of :
.
.
Notice that both and
are first derivatives of
over the interval
.
However, among these two zeros, only ensures that the second derivative
is smaller than zero (that is:
.) If the second derivative
is non-negative, that zero of
would either be an inflection point (if
) or a local minimum (if
.)
Therefore would be the only local maximum over the interval
.
Calculate the value of at this local maximum:
.
Compare these three possible maximum values of over the interval
. Apparently,
would maximize the value of
. That is:
gives the maximum value of
over the interval
.
However, note that the maximum over this interval exists because is indeed part of the
interval. For example, the same
would have no maximum over the interval
(which does not include
.)
Answer:
And for this case the interpretation for the slope would be that for every unit that the height in inches increase then the weight in pounds increase 6 units.
For the intercept of 135 represent the amount initial amount of weight for the scale.
Step-by-step explanation:
We assume that they use least squares in order to create the regression equation
For this case we need to calculate the slope with the following formula:
Where:
With these we can find the sums:
And the slope would be:
The means for x and y are given by:
And we can find the intercept using this:
For this case we know that the line adjusted is:
And for this case the interpretation for the slope would be that for every unit that the height in inches increase then the weight in pounds increase 6 units.
For the intercept of 135 represent the amount initial amount of weight for the scale.