The distance between a point
on the given plane and the point (0, 2, 4) is
but since
and
share critical points, we can instead consider the problem of optimizing
subject to
.
The Lagrangian is
with partial derivatives (set equal to 0)
Solve for
:
which gives the critical point
We can confirm that this is a minimum by checking the Hessian matrix of
:
is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.
At this point, we get a distance from (0, 2, 4) of
The coordinates for M is (4,5)
Answer: X=14
Step-by-step explanation:
The leg and hypothesis is the sum of 20. You already have 6. 6 from 20 is 14
Answer:
The three different possible conditions ;
nonalcoholic beer group, 1 beer group, 2 beer group
Step-by-step explanation:
The Independent variable, also known as the predictor variable are variables used to influence and check changes in the dependent or predicted variable as subjects are exposed to the different types or levels of independent variable used in the study.
In the scenario described above, the predictor or independent variables which are used to measure the reaction times of participants to unexpected variables is the independent variable, beacuse these different variables ; nonalcoholic beer, 2 beer will probably affect the response time of the participants which is the dependent variable.
Answers are: choice A, choice C, choice E
Explanation: The leading coefficient is the number that is to the left of the term with the largest exponent, which in this case is 2. The term 3x^2 is the leading term with the coefficient of 3. This is why the leading coefficient is 3 for choice A, choice C, and choice E. Choice B has a leading coefficient of -3 so we can rule that out. Choice D has a leading coefficient of 3, but the constant term is NOT -2. Instead the constant term is +2, so we can rule out choice D as well. The other choices that haven't been eliminated all have 3x^2 somewhere in them, as well as the constant term -2. The other x term isn't relevant to the restrictions placed in the instructions.
