Answer:
<u>option 1</u>
Step-by-step explanation:
The question is as shown in the attached figure.
From the figure, we can deduce that:
∠U ≅ ∠X and ∠W ≅ ∠Z and ∠V ≅ ∠Y
So, ΔUWV similar to ΔXZY
But it is required to know " How can the triangles be proven similar by the SSS similarity theorem? "
So, we need to prove the corresponding angles are proportion
With the help of the previous corresponding angles.
So, we need to show that the ratios are equivalent.
So, the answer is <u>option 1</u>
The arc length of the curve is
which has a value of about 5.99086.
Let . Split up the interval of integration into 10 subintervals,
[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]
The left and right endpoints are given respectively by the sequences,
with .
These subintervals have midpoints given by
Over each subinterval, we approximate with the quadratic polynomial
so that the integral we want to find can be estimated as
It turns out that
so that the arc length is approximately
Answer:
a. P(X ≤ 5) = 0.999
b. P(X > λ+λ) = P(X > 2) = 0.080
Step-by-step explanation:
We model this randome variable with a Poisson distribution, with parameter λ=1.
We have to calculate, using this distribution, P(X ≤ 5).
The probability of k pipeline failures can be calculated with the following equation:
Then, we can calculate P(X ≤ 5) as:
The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as: