)in flying the 76 miles from champaign to peoria, a student pilot sets a heading that is 11° off course and maintains an average speed of 112 miles per hour. after 15 minutes, the instructor notices the course error and tells the student to correct his heading. through what angle will the plane move to correct the heading and how many miles away is peoria when the plane turns?

Step-by-step explanation:

The law of cosines can be used to find the remaining distance (c). It is given by ...

  c² = a² +b² -2ab·cos(C)

where we have a=76, b=112/4 = 28, C=11°.

  c² = 76² +28² -2·76·28·cos(11°) ≈ 2382.195

  c ≈ √(2382.195) ≈ 48.8 . . . . miles

By the law of sines, ...

  sin(A)/a = sin(C)/c

  sin(A) = (a/c)sin(C)

If you draw a diagram of the problem, you realize that angle A is obtuse. The arcsin function does not return obtuse angles, so an adjustment must be made.

  A = arcsin(a/c·sin(C)) = arcsin(76/48.8·sin(11°)) ≈ 180° -17.3°

The angle through which the plane must turn is the supplement of angle A, so is 17.3°.

81 seats

step-by-step explanation:

if you multiply 0.65 times 125 then you get 81.5 seats. well since you can't have half of a seat you have to round down and get 81 seats in the no children zones. that leave 44 seats outside of the no children zone.

answer: answer is b.

[m < b = 120º]

step-by-step explanation: