Owen has enough materials to build up to 10 birdhouses in shop class. each birdhouse needs 12 square feet of wood. the function w(b) = 12b represents the total amount of wood that owen would need to build b birdhouses. what domain and range are reasonable for the function? a: d: 10 ≤ b ≤ 12 r: 0 ≤ w(b) ≤ 120 b: d: 0 ≤ b ≤ 10 r: 12 ≤ w(b) ≤ 120 c: d: 0 ≤ b ≤ 120 r: 0 ≤ w(b) ≤ 10 d: d: 0 ≤ b ≤ 10 r: 0 ≤ w(b) ≤ 120

W(b) = 12b.

he has enough to build 10 birdhouses, he doesn't have for more than that, he can either build no birdhouses or build 10 birdhouses, since "b" is the independent variable and thus the domain will come from it, what values can "b" safely take?   "b" can be either 0 or more than 0 but nor more than 10, because Owen doesn't have enough for more than that, 0 ≤ b ≤ 10.

let's say owen chooses to build 0 birdhouses, then W(0) = 12(0) => W(0) = 0.

let's say owen chooses to build 10 birdhouses, then W(10) = 12(10) => W(10) = 120.

so the amount of wood needed for those birdhouses, namely the range, can be either 0, if he chooses to build none, or 120 if he chooses to build 10, 0 ≤ W(b) ≤ 120.

sorry not knowing about that

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen