The perimeter of the original rectangle on the left is 30 meters. The perimeter of the reduced rectangle on the right is 24 mete
2 answers:
Answer:
5 meters
Step-by-step explanation:
If the smallest rectangle has a length of 8 meters, and a perimeter of 24 meters then its width is given by:
We can conclude that the width is half of the length for both rectangles. Therefore, the width of the larger rectangle, with a perimeter of 30 meters, is:
The width of the original rectangle is 5 meters.
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Answer:
So the approximate relative minimum is (0.4,-58.5).
Step-by-step explanation:
Ok this is a calculus approach. You have to let me know if you want this done another way.
Here are some rules I'm going to use:
(Sum rule)
(Constant multiple rule)
(Power rule)
(Constant rule)
(Slope of y=x is 1)
Now we set y' equal to 0 and solve for the critical numbers.
Divide both sides by 2:
Compaer to
to determine the values for
.
We are going to use the quadratic formula to solve for our critical numbers, x.
Let's separate the choices:
Let's approximate both of these:
.
This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.
The relative maximum is at approximately -2.5576505.
So the relative minimum is at approximate 0.3909838.
We could also verify this with more calculus of course.
Let's find the second derivative.
So if f''(a) is positive then we have a minimum at x=a.
If f''(a) is negative then we have a maximum at x=a.
Rounding to nearest tenths here: x=-2.6 and x=.4
Let's see what f'' gives us at both of these x's.
So we have a maximum at x=-2.6.
So we have a minimum at x=.4.
Now let's find the corresponding y-value for our relative minimum point since that would complete your question.
We are going to use the equation that relates x and y.
I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.
I'm shoving this into a calculator:
So the approximate relative minimum is (0.4,-58.5).
If you graph you should see the graph taking a dip at this point.