Given f(x) = 5 - x?, find f(3).
2 answers:
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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:
35 different selections of soundtracks are possible
Step-by-step explanation:
Total number of soundtracks available at the store = 7
Enny decides to purchase 3 movie soundtracks.
So, in this problem we have to find in how many ways can Enny chose 3 soundtracks out of 7. The order in which the soundtracks are chosen does not matter e.g soundtracks A,B and C are the same as soundtracks B,C and A.
In an arrangement when the order does not matter, we use combinations to find the total possible number of arrangements or selections.
So, for this problem choosing 3 soundtracks out of 7 means forming combinations from 7 objects taken 3 at a time. This can be represented mathematically as:
The general formula for combinations is:
Using the values, we get:
This means, Enny can make 35 different selections of soundtracks.