Consider the system of linear equations. x + y = 9.0 0.50 x + 0.20 y = 4.05 Find the values of x and y .
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The Given Sequence is an Arithmetic Sequence with First term = -19
⇒ a = -19
Second term is -13
We know that Common difference is Difference of second term and first term.
⇒ Common Difference (d) = -13 + 19 = 6
We know that Sum of n terms is given by :
Given n = 63 and we found a = -19 and d = 6
The Sum of First 63 terms is 10521
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.