Derive a formula for the bullet speed v in terms of D, T, and a measured angle θ between the position of the hole in the first d
isk and that of the hole in the second. If required, use π, not its numeric equivalent. Both of the holes lie at the same radial distance from the shaft. θ measures the angular displacement between the two holes; for instance, θ=0 means that the holes are in a line and θ=π means that when one hole is up, the other is down. Assume that the bullet must travel through the set of disks within a single revolution.
1 answer:
You might be interested in
Using the z-table, the probability that a student taking this test will finish in 100 minutes or less is 0.0824 or 8.24%.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 100
μ = mean = 125
σ = standard deviation = 18
z-score = (100 – 125) / 18
z-score = (-25) / 18
z-score = -1.39
Find the probability that corresponds to the z-score in the z-table. (see attached images)
-1.39 - (-1.3) : -1.4 - (-1.3) = x - 0.0968 : 0.0808 - 0.0968
-0.09 : -0.1 = x - 0.0968 : -0.016
x - 0.0968 = -0.09(-0.016)/-0.1
x = -0.0144 + 0.0968
x = 0.0824
x = 0.0824
Hence, the probability that a student taking this test will finish in 100 minutes or less is 0.0824 or 8.24%.
Learn more about probability here: brainly.com/question/26822684
#SPJ4
Answer:
a) The system has a unique solution for and any value of
, and we say the system is consisted
b) The system has infinite solutions for and
c) The system has no solution for and
Step-by-step explanation:
Since we need to base the solutions of the system on one of the independent terms (), the determinant method is not suitable and therefore we use the Gauss elimination method.
The first step is to write our system in the augmented matrix form:
The we can use the transformation , obtaining:
.
Now we can start the analysis:
- If
then, the system has a unique solution for any value of
, meaning that the last row will transform back to the equation as:
from where we can see that only in the case of the value of
can not be determined.
- if
and
the system has infinite solutions: this is very simple to see by substituting these values in the equation resulting from the last row:
which means that the second equation is a linear combination of the first one. Therefore, we can solve the first equation to get
as a function of
o viceversa. Thus,
(
) is called a parameter since there are no constraints on what values they can take on.
if and
the system has no solution. Again by substituting in the equation resulting from the last row:
which is false for all values of
and since we have something that is not possible
the system has no solution