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I think the answer might be in the photo but we would need to see what we’re working with lol
Answer:
0.2287
Step-by-step explanation:
The computation of the probability that the automated manufacturing system runs for more than 18 hours without a failure is shown below:
P(X > 17) = 1 - P(X < 17)
= 1 - [1 - e^-18 ÷ 12.2]]
= 1 - [1 -0.228684984
]
= 0.2287
First no. = x
Second no. = y
Equation Formation
x + y = 55..........equation (i)
x - y = 1..............equation (i)
x = 1+y
1 + y + y = 55
1 + 2 y = 55
2 y = 55-1
2 y = 54
y = 27
x=27 + 1
x =28
Answer = 28 , 27
Integrate sin(3x+1) with respect to x. Use the substitution method. Let u=3x+1 be y our substitution. Then du/dx = 3, and du = 3dx.
Then we have "integrate sin u with respect to u" . Here's where things are just a bit tricky at first. You have "integrate sin (3x+1) with respect to x." If u = 3x+1, then du/dx = 3 and du=3dx. But we don't have 3dx; we have only dx. Manipulate du=3dx as follows: du/3 = dx.
Then, "integral of sin (3x+1) dx" => "integral of sin u (du/3)"
and this is equivalent to (1/3) "integral of sin u du." We get:
(1/3)(-cos u) + c, or (-1/3)*cos u + c. Finally, subst. 3x+1 for du, obtaining
(-1/3)*cos(3x+1) + C (answer).
You should find the derivative of this as a check. If the result of your differentiation is sin(3x+1), your integral was correct. Otherwise, it's not.
Don't worry... this material becomes much easier once you've gotten the knack of it.
