A ball is thrown from the top row of seats in a stadium. The function h(t) = –16t2 + 16t + 96 gives the height, h, in feet, of t
he ball t seconds after it is thrown. How long will it be before the ball hits the ground?
1 answer:
Answer:
3 seconds
Step-by-step explanation:
We assume the ground is where h=0, so the equation we need to solve is ...
0 = -16t^2 +16t +96
Dividing by -16 gives ...
0 = t^2 -t -6
Factoring, we get ...
0 = (t -3)(t +2)
This has solutions t=3 and t=-2. Since we know the ball won't land 2 seconds before it is thrown, the solution is ...
It will be 3 seconds before the ball hits the ground.
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Let y = the number of maple trees
The information given is summarized in the following table.
Number Cost/tree Area used CO₂ absorption
----------- ------------- --------------- ----------------------
x $30 600 ft² 650 lb/yr
y $40 900 ft² 300 lb/yr
The amount available to spend is $2100, therefore
30x + 40y ≤ 2100
or
(3/4)x + y ≤ 52.5 (1)
The land available for planting is 45,000 ft², therefore
600x + 900y ≤ 45000
or
(2/3)x + y ≤ 50 (2)
The amount of CO₂ removed per year is
A = 650x + 300y (3)
The shaded area in the graph shown below is the solution region.
Optimum values of A occur at the vertices, as shown.
The maximum removal rate occurs at (70, 3.33) at a rate of 46,500 lb/year.
Because we should have an integral number of trees, we should have
70 spruce and 3 maple trees.
Answer: 70 spruce, 3 maple
Let y = the number of maple trees
The information given is summarized in the following table.
Number Cost/tree Area used CO₂ absorption
----------- ------------- --------------- ----------------------
x $30 600 ft² 650 lb/yr
y $40 900 ft² 300 lb/yr
The amount available to spend is $2100, therefore
30x + 40y ≤ 2100
or
(3/4)x + y ≤ 52.5 (1)
The land available for planting is 45,000 ft², therefore
600x + 900y ≤ 45000
or
(2/3)x + y ≤ 50 (2)
The amount of CO₂ removed per year is
A = 650x + 300y (3)
The shaded area in the graph shown below is the solution region.
Optimum values of A occur at the vertices, as shown.
The maximum removal rate occurs at (70, 3.33) at a rate of 46,500 lb/year.
Because we should have an integral number of trees, we should have
70 spruce and 3 maple trees.
Answer: 70 spruce, 3 maple