Answer:
x = 3 ± √5
Step-by-step explanation:
The expression (x - 3)² = 5 doesn't need completing the square to solve (this is the step after you finish completing the square):
Step 1: Square root both sides
x - 3 = ±√5
Step 2: Add 3 to both sides
x = 3 ± √5 = 0.76392, 5.23607
Answer:
2 and -1
Step-by-step explanation:
sum = 2 + (-1)
= 1
product = 2 × ( -1)
= -2
Answer:
15150 is the required sum.
Step-by-step explanation:
Gauss method of summing sequences like this is to add the first term to the last term, the second term to the second to the last term and so on until you get to the middle. By doing this, you will always get the same sum. Then you divide the number of terms by two, because you are technically adding the first half of the sequence to the second half. You then multiply the sum of each pair that gave the same number with the number of terms that has been divided by 2. For this problem we have:
3 + 300 = 303
6 + 297 = 303
9 + 294 = 303
and so on.
100÷ 2 = 50.
Therefore we have 50 * 303 = 15150 is the required sum.
Answer:
And we can calculate this with the complement rule like this:
And using the cdf we got:
![P(X>2) = 1- [1- e^{-\lambda x}] = e^{-\lambda x} = e^{-\frac{1}{2.725} *2}= 0.480](https://tex.z-dn.net/?f=%20P%28X%3E2%29%20%3D%201-%20%5B1-%20e%5E%7B-%5Clambda%20x%7D%5D%20%3D%20e%5E%7B-%5Clambda%20x%7D%20%3D%20e%5E%7B-%5Cfrac%7B1%7D%7B2.725%7D%20%2A2%7D%3D%200.480)
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
And 0 for other case. Let X the random variable of interest:
Solution to the problem
We want to calculate this probability:
And we can calculate this with the complement rule like this:
And using the cdf we got:
the vertical component of the casting velocity will be reduce to zero at point h by the force of gravity.
If we use the kinematic equation
vf² = vi² +2as
and realize that the final vertical velocity is zero
and the initial vertical velocity is vsinθ
where θ is the angle of cast above the horizon
0 = vsin25 + 2(-9.8)h
h = 0.423v / 19.6
h = 0.02156v
so the missing potential heights and the associated answer velocities are
v = 19 m/s...h = 0.410 m
v = 8.3 m/s...h = 0.179 m
v = 6.9 m/s...h = 0.149 m
v = 8.4 m/s...h = 0.181 m
choose the one that fits the question
or use the method to find the correct velocity based on the actual height reference frame.
