Answer:
The given graph shows the relationship between the f(x) and g(x).
Since the problem is to find the points where f(x) becomes equal to g(x) then we will be focusing only to the x-axis and ignore the points of y-axis.
Out of the four choices, the correct answer for the given functions of x will be f(2) = g(2) and f(0) = g(0), f(0) and g(0) is located at the origin. So the points where the curve and line are intersecting is at f(2) and g(2) and the other point is at f(0) and g(0), neglecting the y-axis.
Step-by-step explanation:
Lets call the number 'n'
plus means addition
is means the equal sign
so that as an expression would be
n+4=7
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.
Let x represent the length of the shortest side. Then the perimeter is
.. x +2x +(x +13) = 149
.. 4x = 136
.. x = 34
2x = 68
x+13 = 47
The lengths of the sides are 34, 47, and 68 ft.
While x is the number of small shakes and y is the number of large shakes each size shake you by needs to be multiplied by the cost .... D: 3x+5y=479
