Find the missing side length assuming lines that appear to be tangent are tangent. Show work on piece of paper.
1 answer:
Answer:
20
Step-by-step explanation:
Since the line of length 16 is a tangent to the circle, then the angle between it and the radius is right.
? is the hypotenuse of the right triangle formed.
Using Pythagoras' identity on the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
?² = 12² + 16² = 144 + 256 = 400 ( take the square root of both sides )
? = = 20
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Answer:
(a)
(b)
(c) x=12
(d)Optimal ticket price: $12
Maximum Revenue:$360,000
Step-by-step explanation:
The stadium holds up to 50,000 spectators.
When ticket prices were set at $12, the average attendance was 30,000.
When the ticket prices were on sale for $10, the average attendance was 35,000.
(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)
Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).
Therefore, we have:
At point (12,30000)
Therefore:
(b)Revenue
(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.
The critical value of R(x) is x=12.
(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]
Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.
Therefore:
- Optimal ticket price:$12
- Maximum Revenue:$360,000