Find the domain and range of f(x) = 2 square root of x-2
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Jacob wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn,so he needs no fence on that side.
Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn).
one side of the length is not counted for perimeter because one side of length will be against the barn.
Perimeter = 400 ft
Perimeter of rectangle = L + W + W
400 = L + 2W
L = 400 - 2W
Area = L * W
Replace L by 400 - 2W
A(W) = (400 - 2W) * W
Now we find out x coordinate of vertex to find the width that maximize the area
a= -2 and b = 400
The width w would maximize the area is w = 100ft
To find maximum area we plug in 100 for W in A(W)
the maximum area is 20,000 square feet
Let's call a child's ticket and an adult's ticket
. From this, we can say:
,
since 116 tickets are sold in total.
Now, we are going to need to find another equation (the problem asks us to solve a systems of equations). This time, we are not going to base the equation on ticket quantity, but rather ticket price. We know that an adult's ticket is $17,000, and a child's ticket is thus
.
Given these values, we can say:
,
since each adult ticket costs 17,000 and each child's ticket
costs 12,750, and these costs sum to 1,653,250.
Now, we have two equations:
Let's solve:
- Find
on its own, which will allow us to substitute it into the first equation
- Substitute in
for
- Apply the Distributive Property
- Combine like terms
- Subtract 1972000 from both sides of the equation and multiply both sides by -1
We have now found that 75 child's tickets were sold. Thus,
,
41 adult tickets were sold as well.
In sum, 41 adult tickets were sold along with 75 child tickets.