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2 answers:
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The equation of the lines can be plotted on the graph after calculating the coordinates on each line.
<h3>What is a linear equation?</h3>It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have two linear equation:
x = 4y
x + y = 7.0
To plot the linear equation first we will find the few coordinates to plot on the coordinate plane.
For the equation of line:
x = 4y
x 0 1 2 3 -1 -2 -3
y 0 4 8 12 -4 -8 -12
For the equation of line:
x + y = 7.0
x 0 1 2 3 -1 -2 -3
y 7 6 5 4 8 9 10
Thus, the equation of the lines can be plotted on the graph after calculating the coordinates on each line.
Learn more about the linear equation here:
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Answer:
The maximum volume of the open box is 24.26 cm³
Step-by-step explanation:
The volume of the box is given as , where
and
.
Expand the function to obtain:
Differentiate wrt x to obtain:
To find the point where the maximum value occurs, we solve
Discard x=3.54 because it is not within the given domain.
Apply the second derivative test to confirm the maximum critical point.
,
This means the maximum volume occurs at .
Substitute into
to get the maximum volume.
The maximum volume of the open box is 24.26 cm³
See attachment for graph.
