Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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)=13hR(h)=\sqrt{13h} gives the distance, in kilometers, that Skyler can see when their eyes are hh meters above the ground.\newlineThe function A(d)=πd2A(d)=\pi d^{2} gives the area, in square kilometers, that Skyler can guard when they can see a distance of dd kilometers.\newlineWhich expression models the area Skyler can guard when their eyes are hh meters above the ground?\newlineChoose 11 answer:\newline(A) 13πh13\pi h\newline(B) 13πh213\pi h^{2}\newline(C) 13πh2\sqrt{13\pi h^{2}}\newline(D) 169πh2169\pi h^{2}

Full solution

Q. Skyler climbs a watchtower to guard against forest fires.\newlineThe function R(h)=13hR(h)=\sqrt{13h} gives the distance, in kilometers, that Skyler can see when their eyes are hh meters above the ground.\newlineThe function A(d)=πd2A(d)=\pi d^{2} gives the area, in square kilometers, that Skyler can guard when they can see a distance of dd kilometers.\newlineWhich expression models the area Skyler can guard when their eyes are hh meters above the ground?\newlineChoose 11 answer:\newline(A) 13πh13\pi h\newline(B) 13πh213\pi h^{2}\newline(C) 13πh2\sqrt{13\pi h^{2}}\newline(D) 169πh2169\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. Substitute into Area Function: Next, we substitute the expression for R(h)R(h) into the function A(d)A(d) to find the area Skyler can guard. So we replace dd with 13h\sqrt{13h} in the function A(d)=πd2A(d) = \pi d^2.
  3. Calculate Area Function: Now, we calculate the area function A(13h)A(\sqrt{13h}) by squaring the distance function R(h)R(h). This gives us A(13h)=π(13h)2A(\sqrt{13h}) = \pi(\sqrt{13h})^2.
  4. Simplify Area Expression: Squaring the square root will cancel out the square root, leaving us with A(13h)=π(13h)A(\sqrt{13h}) = \pi(13h).
  5. Final Area Model: Therefore, the expression that models the area Skyler can guard when their eyes are hh meters above the ground is A=13πhA = 13\pi h, which corresponds to option (A)(A).

More problems from Area of quadrilaterals and triangles: word problems