A man is flying in a hot-air balloon in a straight line while keeping it at a constant altitude. As he approaches a parking lot and notices that the angle of depression from his balloon to a friend's car is 36º. He flew directly over the car. A minute and a half later he had travelled 360 feet horizontally; he looks back to see his friend getting into the car and observes the angle of depression to be 37º. At that time, what is the distance between him and his friend?

221°

Step-by-step explanation:

Using sine rule

a/sinA = b/sinB = c/sinC

A= 36°

B= 37°

C = 107°

It takes 90 seconds to go from point A to point B. To find a, we will use

a/sinA = c/sinC

a/sin36°= 360/sin 107°

a(sin 107°) = 360sin36°

a = 360sin 36° / sin 107°

a = 360(0.5878) / 0.9563

a = 211.608/0.9563

a = 221.27°

a = 221°

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.