Take partial derivatives and set them equal to 0:
We find one critical point within the boundary of the disk at
. The Hessian matrix for this function is
which is positive definite, and incidentally independent of
and
, so
attains a minimum
.
Meanwhile, we can parameterize the boundary by
with
, which gives
with critical points at
At these points, we get
so we attain a maximum only when
, which translates to
.
Answer:
1) The linear regression model is y = -0.0348·x + 13.989
2) The correlation coefficient is -0.0725
3) The strength of the model is strong - association
Step-by-step explanation:
1)
X Y XY X²
27 13 351 729
65 12 780 4225
83 11 913 6889
109 10 1090 11881
142 9 1278 20164
175 8 1400 30625
∑ 601 63 5812 74513
From y = ax + b, we have
b = 1/n(∑y -a∑x) = 1/6(63 - (0.0348)×601) = 13.989
Therefore, the linear regression model is y = -0.0348·x + 13.989
2)
![r = \frac{n\sum xy - \sum x\sum y }{\sqrt{[n\sum x^{2}-\left (\sum x \right )^{2}] [n\sum y^{2}-\left (\sum y \right )^{2}]}} = \frac{6 \times 5812 - 601 \times 63}{\sqrt{[6 \times 74513-601^{2}] [6 \times 3969 - 63^2]} } = - 0.0725](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bn%5Csum%20xy%20-%20%5Csum%20x%5Csum%20y%20%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E%7B2%7D-%5Cleft%20%28%5Csum%20x%20%20%5Cright%20%29%5E%7B2%7D%5D%20%5Bn%5Csum%20y%5E%7B2%7D-%5Cleft%20%28%5Csum%20y%20%20%5Cright%20%29%5E%7B2%7D%5D%7D%7D%20%20%3D%20%5Cfrac%7B6%20%5Ctimes%205812%20%20-%20601%20%5Ctimes%2063%7D%7B%5Csqrt%7B%5B6%20%5Ctimes%2074513-601%5E%7B2%7D%5D%20%5B6%20%20%5Ctimes%203969%20-%2063%5E2%5D%7D%20%7D%20%3D%20-%200.0725)
3) The strength is - association.
Answer : 60x
15x^2/y × 4y^2/xy
60x^2y^2/xy^2
60x
An exercise ball, also known as a yoga ball, is a ball constructed of soft elastic with a diameter of approximately 35 to 85 centimeters (14 to 34 inches) and filled with air. The air pressure is changed by removing a valve stem and either filling with air or letting the ball deflate. It is most often used in physical therapy, athletic training and exercise. It can also be used for weight training. The ball, while often referred to as a Swiss ball, is also known by a number of different names, including balance ball, birth ball, body ball, ball, fitness ball, gym ball, gymnastic ball, physio ball, pilates ball, naval mine, Pezzi ball, stability ball, Swedish ball, or therapy ball.
1. angle 1 = 50 degrees [ Reason is Given]
2. angle 1 and angle 5 are corresponding angles [Given]
3..Therefore angle1=angle 5 [ Corresponding angles are =]
4..Therefore angle 5 = 50 degrees [= angles have same measure]
The above assumes that we are talking about corresponding angles of congruent or similar polygons or corresponding angles forme when a transversal intersects two parallel lines
