(a) Yes all six trig functions exist for this point in quadrant III. The only time you'll run into problems is when either x = 0 or y = 0, due to division by zero errors. For instance, if x = 0, then tan(t) = sin(t)/cos(t) will have cos(t) = 0, as x = cos(t). you cannot have zero in the denominator. Since neither coordinate is zero, we don't have such problems.
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(b) The following functions are positive in quadrant III:
tangent, cotangent
The following functions are negative in quadrant III
cosine, sine, secant, cosecant
A short explanation is that x = cos(t) and y = sin(t). The x and y coordinates are negative in quadrant III, so both sine and cosine are negative. Their reciprocal functions secant and cosecant are negative here as well. Combining sine and cosine to get tan = sin/cos, we see that the negatives cancel which is why tangent is positive here. Cotangent is also positive for similar reasons.
Answer:
a) ![r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%28333%29-%28200%29%285.37%29%7D%7B%5Csqrt%7B%5B4%2812000%29%20-%28200%29%5E2%5D%5B4%289.3501%29%20-%285.37%29%5E2%5D%7D%7D%3D0.9857)
The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables
b) 
Now we can find the means for x and y like this:
So the line would be given by:
Step-by-step explanation:
Part a
The correlation coeffcient is given by this formula:
![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D)
For our case we have this:
n=4 
The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables
Part b
Where:
With these we can find the sums:
And the slope would be:
Now we can find the means for x and y like this:
And we can find the intercept using this:
So the line would be given by:
3/7, 3/5, 1/2 is the answer it starts from the lowest to the lagest
Answer:
16,00
Step-by-step explanation:
9 years is the (time)
divide the 27 years by 9 to see how many times it doubles
the ans is 3
now simply divide the value which is $4,800 by the 3
this gives you 1,600
