Answer:
Explanation:
a). The scale in the art student's drawing is 1 centimeter to represent 3 meters in real height. If the actual height of Arizona Stadium is 71.7 meters tall, we can use the scale to determine the height in the drawing.
To find the height in the drawing, we can set up a proportion:
1 centimeter / 3 meters = x centimeters / 71.7 meters
Simplifying the proportion, we have:
1/3 = x/71.7
Cross-multiplying, we get:
x = (1/3) * 71.7
x ≈ 23.9 centimeters
Therefore, the height of Arizona Stadium in the art student's drawing will be approximately 23.9 centimeters.
b) To create a function h(x) that indicates the height of a location x meters above the ground, we can use the same scale. Since 1 centimeter represents 3 meters, the function can be defined as:
h(x) = (1/3) * x
c) Evaluating h(30), we substitute x = 30 into the function:
h(30) = (1/3) * 30
h(30) = 10 centimeters
This means that a location 30 meters above the ground will be represented as 10 centimeters from the bottom of the scale drawing.
d) To find the value of x such that h(x) = 8, we can set up the equation:
8 = (1/3) * x
Multiplying both sides by 3, we get:
24 = x
Therefore, when h(x) = 8, the value of x is 24. This means that a location 24 meters above the ground will be represented as 8 centimeters from the bottom of the scale drawing.
e) The practical domain for this function represents the possible values for x, which in this case would be the height above the ground. Since the height can be any positive value, the domain is (0, ∞) in interval notation.