Which of the following equations will produce the graph shown below?
2 answers:
The graph is a circle, centered at the origin, with radius=4.
We know that we can write the equation of a circle with radius r and center (a,b) as :
.
Thus, substituting (a, b) with (0, 0) and r with 4, we have:
.
The solutions of this equation are all the points forming the circle shown in the picture. The solutions of this equation are still the same even if we multiply both sides of the equation by 2, because rewriting the equation as:
,
we would still have the same roots.
Thus, the equation of the circle can be written as :
.
Answer: B
We know that we can write the equation of a circle with radius r and center (a,b) as :
Thus, substituting (a, b) with (0, 0) and r with 4, we have:
The solutions of this equation are all the points forming the circle shown in the picture. The solutions of this equation are still the same even if we multiply both sides of the equation by 2, because rewriting the equation as:
we would still have the same roots.
Thus, the equation of the circle can be written as :
Answer: B
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Given:- ;
, where a is any positive real number.
Consider the helix parabolic equation :
now, take the derivatives we get;
As, we know that two vectors are orthogonal if their dot product is zero.
Here, are orthogonal i.e,
Therefore, we have ,
take t common in above equation we get,
⇒ or
To find the solution for t;
take
The number determined from the coefficients of the equation
The determinant
Since, for any positive value of a determinant is negative.
Therefore, there is no solution.
The only solution, we have t=0.
Hence, we have only one points on the parabola i.e <1,0>
Answer:
X is the GPA
Y is the Salary
Standard deviation of X is 0.4
Standard deviation of Y is 8500
E(X)=2.9
E(Y)=47200
We are given that The correlation between the two variables was r = 0.72
a)
So, slope = 15300
Intercept = 2830
So, equation :
b) Your brother just graduated from that college with a GPA of 3.30. He tells you that based on this model the residual for his pay is -$1880. What salary is he earning?
Observed salary = Residual + predicted = -1860+53320 = 51440
c)) What proportion of the variation in salaries is explained by variation in GPA?
The proportion of the variation in salaries is explained by variation in GPA =