Answer:
3 ln(x − 1) − 3/(x − 1) + C
Step-by-step explanation:
∫ 3x / (x − 1)² dx
3 ∫ x / (x − 1)² dx
If u = x − 1, then x = u + 1, and du = dx.
3 ∫ (u + 1) / u² du
3 ∫ (1/u + 1/u²) du
3 (ln u − 1/u + C)
3 ln u − 3/u + C
Substitute back:
3 ln(x − 1) − 3/(x − 1) + C
Answer:
A
Step-by-step explanation:
Notice how it points it out for the x coordinate, and the closed circle means that point is included, So it's the range of the smallest x coordinate to the greatest x coordinate.
Answer:
5 (grandson's age now)
35 (son's age now)
60 (father's age now)
Step-by-step explanation:
Answer: 0.16
Step-by-step explanation:
Given that the run times provided are normally distributed ;
Mean(x) of distribution = 3 hours 50 minutes
Standard deviation(s) = 30 minutes
The probability that a randomly selected runner has a time less than or equal to 3 hours 20 minutes
3 hours 20 minutes = (3 hrs 50 mins - 30 mins):
This is equivalent to :
[mean(x) - 1 standard deviation]
z 1 standard deviation within the mean = 0.84
z, 1 standard deviation outside the mean equals:
P(1 - z value , 1standard deviation within the mean)
1 - 0.8413 = 0.1587
= 0.16
