a biologist record the population growth of two species of frog in the atea starting in 2010 the first started with 42 frog and increased by 6 frogs per year the second species started with 30 frogs an increased by 8 foot per year write an equation modeling equal populations of the frogs t years after 2010

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