Fire load (MJ/m2) is the heat energy that could be released per square meter of floor area by combustion of contents and the str
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This issue involves a basic dimensional analysis. We are required to express the rate of 0.992 atm/m in the unit of atm/km.
In straightforward terms, dimensional analysis means converting a measurement into a different unit using conversion factors.
For this case, the necessary steps are:
We observe that 1000 meters = 1 kilometer was used as the conversion factor to change atm/m into atm/km. Consequently, we conclude with the answer 992 atm/km.
In straightforward terms, dimensional analysis means converting a measurement into a different unit using conversion factors.
For this case, the necessary steps are:
We observe that 1000 meters = 1 kilometer was used as the conversion factor to change atm/m into atm/km. Consequently, we conclude with the answer 992 atm/km.
Answer:
Part 1) The equation is
Part 2) When x=40 m, the area of the schoolyard is A=2,800 m^2
Part 3) The valid domain consists of all real numbers exceeding zero and below 75 meters
Step-by-step explanation:
Part 1) Formulate an expression for A(x)
Let
x -----> the length of the rectangular school yard
y ---> the width of the rectangular school yard
It is known that
The perimeter for the fencing (taking the school wall as one side) is
thus
-----> this is equation A
The area of the rectangular school yard is
----> this is equation B
Substituting equation A into equation B yields
Change to function notation
Part 2) What is the area when x=40?
With x equal to 40 m
substitute the value into the expression from Part 1 to determine A
Part 3) What would be a suitable domain for A(x) in this scenario?
We understand that
A signifies the area of the rectangular school yard
x characterizes the length of the rectangular school yard
It follows that
This forms a vertical parabola opening downwards
The vertex indicates a maximum point
The x-coordinate of the vertex corresponds to the length that maximizes the area
The y-coordinate of the vertex denotes the maximum area
The vertex corresponds to (37.5, 2812.5)
Refer to the accompanying figure
Consequently,
The peak area achieved is 2,812.5 m^2
The x-intercepts are located at x=0 m and x=75 m
The domain for A is the range -----> (0, 75)
All real numbers greater than zero and less than 75 meters
