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).Substitute into Area Function: Next, we substitute the expression for R(h) into the function A(d) to find the area Skyler can guard. So we replace d with sqrt(13h) in the function A(d) = pid^2.Calculate Area Function: Now, we calculate the area function A(sqrt(13h)) by squaring the distance function R(h). This gives us A(sqrt(13h)) = pi(sqrt(13h))^2.Simplify Area Expression: Squaring the square root will cancel out the square root, leaving us with A(sqrt(13h)) = pi(13h).Final Area Model: Therefore, the expression that models the area Skyler can guard when their eyes are h meters above the ground is A = 13pih, which corresponds to option (A).

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