So, f[x] = 1/4x^2 - 1/2Ln(x)
<span>thus f'[x] = 1/4*2x - 1/2*(1/x) = x/2 - 1/2x </span>
<span>thus f'[x]^2 = (x^2)/4 - 2*(x/2)*(1/2x) + 1/(4x^2) = (x^2)/4 - 1/2 + 1/(4x^2) </span>
<span>thus f'[x]^2 + 1 = (x^2)/4 + 1/2 + 1/(4x^2) = (x/2 + 1/2x)^2 </span>
<span>thus Sqrt[...] = (x/2 + 1/2x) </span>
Answer:

Step-by-step explanation:
Data provided in the question:
Number of cups of tea offered = 3
Number of cups marked = 9
Number of cups tasted by each = 4
Now,
The probability that a contestant does not taste all of the samples
= contestant tastes only 2 samples of tea
=
C₆⁴ = number of ways to choose 4 cups out of 6 cups of two samples
C₃² = number of ways to choose which 2 samples will be tasted
[ as 2 samples × 3 cups each = 6 cups ]
C₉⁴ = Number of ways to choose 4 cups out of 9
= 
Hence,
the correct answer is option (B) 5/14
Answer:
The 3 angles are 62 2/3, 44 2/.3 and 72 2/3 degrees.
Step-by-step explanation:
let x be the first angle then the the second angle is x - 18 and the third angle = x + 10
The 3 angles add up to 180 so:
x + x - 18 + x + 10 = 180
3x = 180 + 18 - 10 = 188
x = 188/3 = 62 2/3 degrees.
x - 18 = 44 2/3
x + 10 = 72 2/3.
$19,905.22 (if the Dealership discount was added after the normal price and the Employee Discount added last)