Solve.x2 = 
A. 
B. 
C. ± 
D. ± 
Answer: C
You might also like to view...
Use the Chain Rule to find  figure.png)
 multiple choice.png)
Graph the pair of parametric equations with the aid of a graphing calculator.x = 3 cos t + cos 3t, y = 3 sin t - sin 3t, 0 ? t ? 2?
A. 
B. 
C. 
D. 
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
A. 
B. 
C. 
D. 
- 
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ? The least-squares line must pass through at least one data point. ?
A. It is false.
?
Example. Find the least-squares line for the data
?
?
Solution. Here, we have 
and
?
 |  |  |  |  |
 |  |  |  |  |
?
?
The least-squares line for the data is given by linear equation
?
?
where the constants m and b satisfy the normal equations
?
?
?
?
Then, we obtain the normal equations
?
?
Solving them, we found 
?
Therefore, the required least-squares line is 
?
The scatter diagram and the least-squares line are shown in the figure. We can see that the line does not pass through any data point.
?
B. It is true
?
Suppose that we are given two data points
?
?
If we try to fit a straight line to these data points, the line will miss the first and the second data points by the amountsd1,d2, respectively.
?
?
The principle of least squares states that the straight line L that fits the data points best is the one chosen by requiring that the sum of the squares
?
?
be made as small as possible. But it is possible only in case when least-squares line passes through at least one data point.