To find the maximum or minimum value of a function, we can find the derivative of the function, set it equal to 0, and solve for the critical points.
H'(t) = -32t + 64
Now find the critical numbers:
-32t + 64 = 0
-32t = -64
t = 2 seconds
Since H(t) has a negative leading coefficient, we know that it opens downward. This means that the critical point is a maximum value rather than a minimum. If we weren't sure, we could check by plugging in a value for t slightly less and slighter greater than t=2 into H'(t):
H'(1) = 32
H'(3) = -32
As you can see, the rate of change of the object's height goes from increasing to decreasing, meaning the critical point at t=2 is a maximum.
To find the height, plug t=2 into H(t):
H(2) = -16(2)^2 +64(2) + 30 = 94
The answer is 94 ft at 2 sec.
y≥25x+2000
because the +2000 is the y intercept ( where he started) and its 25x because he gets 25 over x amount of weeks
Answer:
.
Step-by-step explanation:
Let X be a discrete random variable with geometric distribution.
Let x be the number of tests and p the probability of success in each trial, then the probability distribution is:
P (X = x) = p * (1-p) ^ (x-1). With x = (1, 2, 3 ... n).
This function measures the probability P of obtaining the first success at the x attempt.
We need to know the probability of obtaining the first success at the third trial.
Where a success is defined as a customer buying online.
The probability of success in each trial is p = 0.3.
So:
P (X = 3) = 0.3 * (1-0.3) ^ (3-1)
P (X = 3) = 0.147
The probability of obtaining the first success at the third trial is 14.7%
