is conservative if we can find a scalar function 
such that 
. This is equivalent to solving the system of PDEs,
Integrate both sides of the first PDF with respect to 
:
where 
is some function independent of . Then differentiatng with respect to 
, we have
and so is indeed conservative, with
Given:
The measure of three sides of a triangle are 8, 7 and 14.
To find:
The measure of the angle opposite the side of length 8.
Solution:
According to the Law of Cosine:
Let a=8, b=7 and c=14, then by using Law of Cosine, we get
Taking cos inverse on both sides.
Therefore, the measure of the angle opposite the side of length 8 is 22.6 degrees.
Answer:
f(g(x)) = x
Explanation:
In order to prove that one function is the inverse of the other, all you have to do is substitute in the main function with the inverse one and solve. If the result is x, then it is verified that one function is the inverse of the other.
Now for the given functions we have:
<span>f(x) =5x-25
</span><span>g(x) = (1/5)x+5
We want to prove that g(x) is the inverse of f(x).
Substitute in the above formula and compute the result as follows:
f(g(x)) = 5(</span>(1/5)x+5) - 25
= x + 25 - 25
= x
The final result is "x", therefore, it is verified that g(x) is the inverse of f(x)
Hope this helps :)
Answer:
The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of 
.
A store randomly samples 603 shoppers over the course of a year and finds that 142 of them made their visit because of a coupon they'd received in the mail.
This means that 
95% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).
First distribute in the 2 on the left side to get 6d+6=7+6d
Then, you would combine the variables to be on one side of the equation by doing -6d. However, this would cancel out the d by leaving you with 0d+6=7. That is the same thing as saying 6=7.
The answer to this equation is no solution because 6 is NOT equal to 7.
