How to find function of x
1 answer:
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Let r = (t,t^2,t^3)
Then r' = (1, 2t, 3t^2)
General Line integral is:
The limits are 0 to 1
f(r) = 2x + 9z = 2t +9t^3
|r'| is magnitude of derivative vector
Fortunately, this simplifies nicely with a 'u' substitution.
Let u = 1+4t^2 +9t^4
du = 8t + 36t^3 dt
After integrating using power rule, replace 'u' with function for 't' and evaluate limits:
Then r' = (1, 2t, 3t^2)
General Line integral is:
The limits are 0 to 1
f(r) = 2x + 9z = 2t +9t^3
|r'| is magnitude of derivative vector
Fortunately, this simplifies nicely with a 'u' substitution.
Let u = 1+4t^2 +9t^4
du = 8t + 36t^3 dt
After integrating using power rule, replace 'u' with function for 't' and evaluate limits:
Answer:
The probability is 28 % ( approx )
Step-by-step explanation:
Since, there are only two possible outcomes in every trails ( residents are in their forties or not ),
So, this is a binomial distribution,
Binomial distribution formula,
Probability of success in x trials,
Where,
p and q are probability of success and failure respectively and n is the total number of trials.
Let X be the event of resident who are in his or her forties.
Here, p = 12% = 0.12,
⇒ q = 1 - p = 1 - 0.12 = 0.88,
n = 9,
Hence, the probability that two or three of the people in the group are in their forties = P(X=2) + P(X=3)
Replace x with a couple of numbers, solve for Y them mark those points on the graph and connect with a line.
See picture:
