13pi/12 lies between pi and 2pi, which means sin(13pi/12) < 0
Recall the double angle identity,
sin^2(x) = (1 - cos(2x))/2
If we let x = 13pi/12, then
sin(13pi/12) = - sqrt[(1 - cos(13pi/6))/2]
where we took the negative square root because we expect a negative value.
Now, because cosine has a period of 2pi, we have
cos(13pi/6) = cos(2pi + pi/6) = cos(pi/6) = sqrt[3]/2
Then
sin(13pi/12) = - sqrt[(1 - sqrt[3]/2)/2]
sin(13pi/12) = - sqrt[2 - sqrt[3]]/2
Answer:
Step-by-step explanation:
The formula for this is the one we use when we are given the ratio the directed line segment is separated into as opposed to the point being, say, one-third of the way from one point to another. The 2 equations we use to find the x and y coordinates of this separating point are:
and
where x1, x2, y1, y2 come from the coordinates of A and B, and a = 1 (from the ratio) and b = 2 (from the ratio). Filling in for x first:
and then y:

The coordinates of point E, then, are (0, 1).
<h2><u>
Answer with explanation:</u></h2>
Let
be the population mean strain in a way that conveys information about precision and reliability.
The sample mean is the best point estimate of the true population mean .
As per given , we have
Sample size : n= 12
degree of freedom : 
Sample mean : 
The true average strain in a way that conveys information about precision and reliability= 25.0
sample standard deviation : s= 3.3
Significance level : 
Since sample population standard deviation is unknown , so we use t-test.
Critical t-value for t : 
95% Confidence interval for true average strain in a way that conveys information about precision and reliability:


The 95% Confidence interval for true average strain in a way that conveys information about precision and reliability: 
We 95% confident that the true population average strain in a way that conveys information about precision and reliability lies between 22.9 and 27.1 .
[2*(10 + 5)] - 5
[2*(15)] - 5
[2(15)] - 5
[30] - 5
25
Answer: (-7,-1)
Complete question is attached below
The coordinates of J is (-15,-5) and K is (25,15)
The formula to find point E (x,y) is


We know the ratio is 1:4
m=1 and n=4
(x1,y1) is (-15,-5) and (x2,y2) is (25,15)
Now plug in all the values in the formula and find out x and y


The point E is (-7,-1)