Answer:
The ball will reach a height of 5 ft by the 4th time.
Step-by-step explanation:
The initial height of the ball is 40 ft, when it bounces from the floor once the height will be 20 ft, the second time it'll be 10 ft, and so on. The sequence that can represent the maximum height of the ball after each bounce is:
{40, 20, 10,...}
This kind of sequence is called a geometric progression, in this kind of progression the next number is related to the one before it by the product of a constant called ratio, in this case 1/2. To calculate a specific position in this sequence we only need the ratio and the first number, using the formula below:
a_n = a*r^(n-1)
Where n is the position we want to know, a is the first number and r is the ratio. In this case we have:
a_4 = 40*(1/2)^(4-1) = 40*(1/2)^3 = 40/8 = 5
The ball will reach a height of 5 ft by the 4th time.
The figure shows that N is the vertex of a right triantle.
The opposite leg to N measures 5.74, the adjacent leg to N measures 4 and the hypotenuse measures 7.
Then you can states these ratios:
sin(N) = opposite leg / hypotenuse = 5.74 / 7 => N = arcsin(5.74 / 7) = arcsin(0.82) = 55.08 °.
cos(N) = adjacent leg / hypotenuse = 4 / 7 => N = arccos(4/7) = 55.15°
tan(N) = opposite leg / adjacent leg = 5.74 / 4 => N = arctan (5.74/4) = 55.13°.
Of course, you do not need to do the three calculations. I did it just to show you.
Answer: the value of N to the nearest whole degree is 55°
