8/9 * 1/7 is 8/63 sooo yeah
Answer:
(−81)(−9) = 729
Step-by-step explanation:
Multiply -81 by -9 and you get 729
Answer:
The farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.
Step-by-step explanation:
The question tests the applications of differential calculus. We are informed that the farmer will use the wall of his barn as one side of the enclosure implying that the 144 feet of fencing will only be used to form the three remaining sides of the rectangular enclosure.
If we let x denote the width of this rectangular enclosure to be formed, then its length will be 144-2x since we shall be having two sides each measuring x and the total length of the fencing is 144. 2x will be used on the width leaving 144-2x for the length since one side of the length is formed by the wall.
If we let A denote the area of the rectangular enclosure, then;
A = x(144 - 2x)
since the area of a rectangle is simply the product of the length and the width. We open the brackets;
A = 144x - 2x^2
Clearly, the Area is a function of the width that is A is the dependent variable while x is the independent one.
At the maximum area, the slope of the tangent to the curve 144x - 2x^2 is 0. Therefore, we differentiate the given function of x with respect to x then set the resulting expression to 0 to determine x that will maximize A;
dA/dx = 144 - 4x
We set this expression to 0 and solve for x;
144 - 4x = 0
144 = 4x
x = 36
Therefore, the farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.
The slope of the line may be calculated by using the formula:
m = (y2 - y1)/(x2 - x1), where m is the slope, and (x1, y1) and (x2, y2) are two points on the line.
Using the points (0, -1) and (2, 4) shown, we can substitute these values into the formula above to get:
m = (y2 - y1)/(x2 - x1)
m = (4 - (-1))/(2 - 0)
m = 5/2
Therefor, the slope is 5/2.
Another way to think about the slope is in terms of rise/run, that is for a given interval that the x-value 'runs', by how much does the y value 'rise'?
Here, if we take the same two points (0, -1) and (2, 4), we can see that the x-value has moved 2 units, and the y-value has increased by 5 units. Thus:
if slope = rise/run, then the slope would be 5/2
Note that you should be careful when using this method if the y-value decreases as x increases; in this scenario, the 'rise' would be a negative value rather than a positive one
