Consider this solution; note, the answer is marked by green colour.
Answer:
$64
Step-by-step explanation:
The tangent of the angle gives the ratio of the height of the lighthouse to the boat's distance
.. tan(angle of depression) = (lighthouse height)/(boat distance)
Then the distance to the boat is
.. boat distance = (lighthouse height)/tan(angle of depression)
We want to find the difference between two distances, so
.. boat travel = (lighthouse height)*(1/tan(first angle) -1/(tan(second angle))
.. = (200 ft)*(1/tan(17°31') -1/tan(46°41'))
.. ≈ 445.10 ft
We need to multiply the factors (x - 2) and (x^2 + 9x + 10) to see if the product is the original expression given.
(x - 2)(x^2 + 9x + 10)
x^3 + 9x^2 + 10x - 2x^2 - 18x - 20
x^3 + 7x^2 - 8x - 20.
Since the product just found is not the original expression given, Jimmy is wrong.
I will complete the work on paper by synthetic division and post my answer.
After using synthetic division, the correct quotient is x^2 + 9x + 20.
