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the height of an arch above the ground is given by the function y=10cosx for x -/2≤X≤/2. what is the average height of the arch above the ground?

User Dee S
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Final answer:

To find the average height of the arch, integrate the given function over the interval (-π/2, π/2). The average height is (1/(π/2 - (-π/2))) * ∫[-π/2 to π/2] 10cos(x) dx.

Step-by-step explanation:

To find the average height of the arch, we need to integrate the function y = 10cos(x) over the given interval. The average height is given by the formula:



Average height = (1/(b-a)) * ∫[a to b] f(x) dx



Plugging in the values for a = -π/2 and b = π/2, we can calculate the average height by evaluating the integral:



Average height = (1/(π/2 - (-π/2))) * ∫[-π/2 to π/2] 10cos(x) dx



We can simplify this equation to find the average height of the arch above the ground.

User Nikravi
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