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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)

Skyler climbs a watchtower to guard against forest fires.\newlineThe function R(h)=13h R(h)=\sqrt{13 h} gives the distance, in kilometers, that Skyler can see when their eyes are h h meters above the ground.\newlineThe function A(d)=πd2 A(d)=\pi d^{2} gives the area, in square kilometers, that Skyler can guard when they can see a distance of d d kilometers.\newlineWhich expression models the area Skyler can guard when their eyes are h h meters above the ground?\newlineChoose 11 answer:\newline(A) 13πh 13 \pi h \newline(B) 13πh2 13 \pi h^{2} \newline(C) 13πh2 \sqrt{13 \pi h^{2}} \newline(D) 169πh2 169 \pi h^{2}

Full solution

Q. Skyler climbs a watchtower to guard against forest fires.\newlineThe function R(h)=13h R(h)=\sqrt{13 h} gives the distance, in kilometers, that Skyler can see when their eyes are h h meters above the ground.\newlineThe function A(d)=πd2 A(d)=\pi d^{2} gives the area, in square kilometers, that Skyler can guard when they can see a distance of d d kilometers.\newlineWhich expression models the area Skyler can guard when their eyes are h h meters above the ground?\newlineChoose 11 answer:\newline(A) 13πh 13 \pi h \newline(B) 13πh2 13 \pi h^{2} \newline(C) 13πh2 \sqrt{13 \pi h^{2}} \newline(D) 169πh2 169 \pi h^{2}
  1. Find Distance Function: First, we need to find the distance Skyler can see when their eyes are hh meters above the ground using the function R(h)=13hR(h) = \sqrt{13h}.
  2. Calculate Guarded Area: We then use the distance found from R(h)R(h) as the input for the function A(d)A(d) to find the area Skyler can guard. The function A(d)=πd2A(d) = \pi \cdot d^2 gives the area in square kilometers for a distance dd in kilometers.
  3. Substitute and Simplify: We substitute R(h)R(h) into A(d)A(d) to get A(R(h))A(R(h)). This means we replace dd with 13h\sqrt{13h} in the area function A(d)A(d).\newlineA(R(h))=π(13h)2A(R(h)) = \pi \cdot (\sqrt{13h})^2
  4. Final 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))=π×(13h)A(R(h)) = \pi \times (13h).
  5. Corresponding Option: The simplified expression is A(R(h))=13×π×hA(R(h)) = 13 \times \pi \times h, which corresponds to option (AA).

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