Answer:
a) 
b) 
c) the points of the form (x, -x) for x≠0
Step-by-step explanation:
a)
If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be
On one hand we have,
On the other hand,
So
b)
The domain of definition of F is
i.e., all the plane X-Y except the (0,0)
c)
Here we want to find all the points such that
where k is a real number other than 0.
But this means
So, all the points in the line y = -x except (0,0) are parallel to the vector field F, that is, the points (x, -x) with x≠ 0
let the number of
Total number of people : adults + children
Total money earned from adults :
Total money earned from children :
Therefore, total money = money earned from each Adult and children.
Now, let's plug the value of x from equation [1] into equation [2]
let's plug the value of y in equation [1]
Hence, we get :
Correct option is C
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Answer:
The predicted life expectancy of men in a country in which the life expectancy of women is 70 years is 65.33 years.
Step-by-step explanation:
The least square regression line is used to predict the value of the dependent variable from an independent variable.
The general form of a least square regression line is:
Here,
<em>y</em> = dependent variable
<em>x</em> = independent variable
<em>α</em> = intercept
<em>β</em> = slope
The regression line to predict the life expectancy of men in a country from the life expectancy of women in that country is:
Compute the life expectancy of men in a country in which the life expectancy of women is 70 years as follows:
Thus, the predicted life expectancy of men in a country in which the life expectancy of women is 70 years is 65.33 years.
C.Quadrilateral is the answer for the following because rhombus, trapezoid, isosceles trapezoid have parallel sides.
Answer: 
which is choice C
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Explanation:
This is a 30-60-90 triangle. The short leg is 5, as it's opposite the smallest angle. The long leg is 
times that of the short leg.
