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:
69.808
Step-by-step explanation:
69.808
ABCD is a parallelogram Given
AE=CE, BE=DE <span>The diagonals of a parallelogram are bisect each other
</span>∠AEB=∠CED Vertical angles are congruent
ΔABE is congruent to ΔCDE SAS theorem<span>
</span>
Answer:
$2,000 or 6.25%
Step-by-step explanation:
1000 x 2 = 2000
28000 + 2000 = 30000 Juan's salary after 2 years
500 x 2 = 1000
31000 + 1000 = 32000 Mariana's salary after 2 years
30000 - 32000 = 2000 difference in salary
2000/32000 x 100= 6.25 difference in salary in percentage
Answer:
Therefore the maximum error in the surface area of the sphere is 22.27 cm².
Therefore the relative error is 0.014 (approx).
Step-by-step explanation:
Given that, The circumference of a sphere was 70 cm with the possible error 0.5 cm.
The circumference of the sphere is C 
∴C 
Differentiating with respect to r
[ relative error = dC= 0.5]
The surface area of the sphere is S= 
∴S=
Differentiating with respect to r
dS will be maximum when dr is maximum.
Putting the value of r and dr
[ ∵ C= 70 ]
⇒dS= 22.27 (approx)
Therefore the maximum error in the surface area is 22.27 cm².
Relative error 
=0.014 (approx)
Therefore the relative error is 0.014 (approx).
