How many times as much does each item cost in 2010 as in 1960 is the movie tix it tickets in 1960 costed $.75 in in 2010 cost 9.
2 answers:
Answer:
13 times.
Step-by-step explanation:
It is given that,
Cost of movie tickets in 1960 = $0.75
Cost of movie tickets in 2010 = $9.75
We need to find how many times as much does each item cost in 2010 as in 1960.
Let x times as much does each item cost in 2010 as in 1960.
Therefore, cost of each item in 2010 is 13 times as in 1960.
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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.