Skyler climbs a watchtower to guard against forest fires. The function R(h)=sqrt(13 h) gives the distance, in kilometers, that Skyler can see when their eyes are h meters above the ground. The function A(d)=pid^(2) gives the area, in square kilometers, that Skyler can guard when they can see a distance of d kilometers. Which expression models the area Skyler can guard when their eyes are h meters above the ground? Choose 1 answer: (A) 13 pi h (B) 13 pih^(2) (c) sqrt(13 pih^(2)) (D) 169 pih^(2)

Question

Skyler climbs a watchtower to guard against forest fires. The function  R(h)=sqrt(13 h) gives the distance, in kilometers, that Skyler can see when their eyes are  h meters above the ground. The function  A(d)=pid^(2) gives the area, in square kilometers, that Skyler can guard when they can see a distance of  d kilometers. Which expression models the area Skyler can guard when their eyes are  h meters above the ground? Choose 1 answer: (A)  13 pi h (B)  13 pih^(2) (c)  sqrt(13 pih^(2)) (D)  169 pih^(2)

Bytelearn · Accepted Answer

Find Distance Function: First, we need to find the distance Skyler can see when their eyes are h meters above the ground using the function R(h) = sqrt(13h).Calculate Guarded Area: We then use the distance found from R(h) as the input for the function A(d) to find the area Skyler can guard. The function A(d) = pi * d^2 gives the area in square kilometers for a distance d in kilometers.Substitute and Simplify: We substitute R(h) into A(d) to get A(R(h)). This means we replace d with sqrt(13h) in the area function A(d). A(R(h)) = pi * (sqrt(13h))^2Final Simplified Expression: We simplify the expression by squaring the square root, which cancels out the square root, leaving us with the expression A(R(h)) = pi * (13h).Corresponding Option: The simplified expression is A(R(h)) = 13 * pi * h, which corresponds to option (A).

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