A quality control officer randomly checking weights of pumpkin seed bags being filled by an automatic filling machine. Each bag
2 answers:
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Answer:
ft/min is the rate of changing of width
Step-by-step explanation:
Given -
The area always remain constant i.2 2 square feet.
Height of the rectangle = 2 feet
Rate of changing of height = 6 feet per minute
Since area is constant
2 sq ft = (2 * 6) ft/min * 1 * x ft/min
x = ft/min
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:
m = - 5
Step-by-step Explanation: