:Jason is tossing a fair coin. He tosses the coin ten times and it lands on heads eight times. If Jason tosses the coin an eleventh time, what is the probability that it will land on heads?
Solution:

The probability would be ½. The result of the eleventh toss does not depend on the previous
results.

6 0

3 years ago

Eben, an alien from the planet Tellurango, kicks a football from field level. The equation for the football’s height in meters,

Luden [163]

The maxima of a differential equation can be obtained by getting the 1st derivate dx/dy and equating it to 0.

Given the equation h = - 2 t^2 + 12 t , taking the 1st derivative result in:

dh = - 4 t dt + 12 dt

dh / dt = 0 = - 4 t + 12 calculating for t:

t = -12 / - 4

t = 3 s

Therefore the maximum height obtained is calculated by plugging in the value of t in the given equation.

h = -2 (3)^2 + 12 (3)

h = 18 m

This problem can also be solved graphically by plotting t (x-axis) against h (y-axis). Then assigning values to t and calculate for h and plot it in the graph to see the point in which the peak is obtained. Therefore the answer to this is:

The ball reaches a maximum height of 18 meters. The maximum of h(t) can be found both graphically or algebraically, and lies at (3,18). The x-coordinate, 3, is the time in seconds it takes the ball to reach maximum height, and the y-coordinate, 18, is the max height in meters.

6 0

3 years ago