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.
I'm assuming the function is f(x) = (2x+8)/(x^2+5x+6). If so, make sure to use parenthesis to indicate that you're dividing all of "2x+8" over all of "x^2+5x+6" as one big fraction. Otherwise, things are ambiguous and it leads to confusion.
Side Note: x^2 means "x squared"
Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)
There are no common factors between the numerator and denominator. So there is nothing to cancel out.
Recall that you cannot divide by zero. Something like 1/0 is undefined.
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3
The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.
Answer:
The answer is (B) $1,307
Step-by-step explanation:
First you would plug the $5000, 5 Years and 8% Interest(Compound) into your Formula - A=P(1+r)t
A=5000(1+.08)5
Which the interest is $2346.64
<u>__ _________________________________________________</u>
Next you would plug $5000, 3 Years and 6.5% Interest(Compound) Into your Formula - A=P(1=r)t
A=5000(1+.065)3
Which the future value is $1039.75
<u>__ _________________________________________________</u>
Finally you would subtract $2346.64 by $1039.75 and then round the difference to the nearest dollar.
Answer:
26. <u>c. 6 cm</u>
27. <u>c. 70 cm³</u>
Step-by-step explanation:
<u>Question 26</u>
- Volume = Length × Width × Height
- 360 = 10 × 6 × Width
- Width = 6 cm
- <u>c. 6 cm</u>
<u></u>
<u>Question 27</u>
- Volume = Length × Width × Height
- Volume = 7 × 5 × 2
- Volume = 70 cm³
- <u>c. 70 cm³</u>
<u></u>
<u>Question 28 (not entirely visible)</u>
