Katherine lives (1 x 100) + (2 x 1) + (8 x 1/10 ) + (4 x 1/100 ) miles away from her grandma. Which number represents the distan
2 answers:
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Answer:
Step-by-step explanation:
<u>Maximization With Derivatives</u>
Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.
We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.
The two divisions parallel to x have lengths y, thus the fencing will take 4x. The three dividers parallel to y have lengths x, thus the fencing will take 3y.
The amount of fence needed to enclose the external and the internal divisions is
We know the total fencing is 1/2 miles long, thus
Solving for x
The total area of the pasture is
Substituting x
Differentiating with respect to y
Equate to 0
Solving for y
And also
Compute the second derivative
Since it's always negative, the point is a maximum
Thus, the maximum area is
Answer:
Hi there!
Recall that slope-intercept form is:
y = mx + b
Where m = slope
In this instance, we are given a slope of 4,
therefore:
y = 4x + b
Substitute in the x and y coordinates of the point given:
0 = 4(3) + b
0 = 12 + b
Substract 12 from both side:
-12 = b
Therefore, the equation would be:
y = 4x - 12
Graph the equation by finding x and y values or using a calculator:
x = 0, y = 4(0) - 12 = 12 (0, 12)
x = 1, y = 4(1) - 12 = - 8 (1, -8)
x = 2, y = 4(2) - 12 = - 4 (2, -4)
x = 3, y = 4(3) - 12 = 0 (3, 0)
And so forth:
Thanks<8
