In the figure, side AB is given by the expression 1 + 3, and side BC is 21 – 4.
1 answer:
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Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.
Answer: The maximum height the football reaches = 51.89 feet.
Step-by-step explanation:
Given: The equation gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked.
Differentiate the given equation, we get
(i)
Put
Differentiate (i) w.r.t. t, we get
< 0 i.e. h is maximum at t= 1.65625
The value of h at t= 1.65625 will be
Hence, the maximum height the football reaches = 51.89 feet.