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.
if its diameter is 34, then its radius is half that or 17.
![\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=17 \end{cases}\implies \begin{array}{llll} SA=4\pi (17)^2\implies SA=1156\pi \\\\\\ SA\approx 3631.68~m^2 \end{array}](https://tex.z-dn.net/?f=%5Ctextit%7Bsurface%20area%20of%20a%20sphere%7D%5C%5C%5C%5C%20SA%3D4%5Cpi%20r%5E2%20~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D17%20%5Cend%7Bcases%7D%5Cimplies%20%5Cbegin%7Barray%7D%7Bllll%7D%20SA%3D4%5Cpi%20%2817%29%5E2%5Cimplies%20SA%3D1156%5Cpi%20%5C%5C%5C%5C%5C%5C%20SA%5Capprox%203631.68~m%5E2%20%5Cend%7Barray%7D)
6,702 = 6 thousands and 7 hundreds and 0 tens and 2 ones
= 6 × 1000 + 7 × 100 + 0 × 10 + 2 × 1
= 6000 + 700 + 2.
Above, we have written the number 6,702 in expanded form, or as a SUM of its different parts according to place value.The digit 6 in the number 6,702 actually has the value 6,000 and the digit 7 actually signifies the value 700. This is why our number system is also called a place value system, because the value of a digit (like 6 or 7 in our example) depends on its placement within the number. In other words, the digit 6 in 6702 does not mean six but six thousand, because the six is placed in the thousands' place. The place of a digit determines its value. I'll go for <span>66.04 that's the closest</span>
I believe that b is right but plz let me know if I am wrong
Your answer :<span>f(x) = one fourth x^2 </span>
