Suppose that there is a positive definite matrix <mrow class="MJX-TeXAtom-ORD"> <mi mathvar

(a) In a regression analysis, the sum of squares for the predicted scores is 100 and the sum of squares error is 200, what is ${\displaystyle R^2}$?
(b) In a different regression analysis, 40% of the variance was explained. The sum of squares total is 1000. What is the sum of squares of the predicted values?

Exercise No. 10 (D.E. with coefficient linear in two variables)
Find the general / solution of the following D.E.
4. $(2x+3y-5)dx+(3x-y-2)dy=0$

Write a multivariable function (i.e z=f(x,y)) for a linear function that contains the points (−1,0),(0,2),(1,−1). Ive

Let ${\displaystyle F(x,y)=⟨4\cos \left(y\right),2\sin \left(y\right)⟩}$. Compute the flux ${\displaystyle \oint F\cdot nds}$ of F across the boundary of the rectangle ${\displaystyle 0\le x\le 5,0\le y\le \frac{\pi }{2}}$ using the vector form of Greens

Solve for x in the equation 5x+4=4-7n.

I have a very simple linear problem:
$\begin{array}{rl}\underset{x}{min}& x^2\\ \text{s.t. }& a_1{x}_1+a_2{x}_2=b\end{array}$
Suppose I want to write this problem equivalently as in Find the equivalent linear program. Unlike the problem in the link, I have equality. Can I write it equivalently as:
$\begin{array}{rl}\underset{x,\alpha ,\beta }{min}& x^2\\ \text{s.t. }& a_1{x}_1=\alpha b,a_2{x}_2=\beta b,\alpha +\beta =1.\end{array}$
The converse is intuitive: Given $\{x,\alpha ,\beta \}$ feasible for the second problem, adding the first and second constraints gives the constraint of the first problem. But the forward part is not clear, especially because I have never seen an equality constraint written like this. Any help would be highly appreciated.

Requires Uploaded Supporting Analysis Find ${\displaystyle \frac{dy}{dx}}$ by implicit differentiation. ${\displaystyle y^2-2x=4y}$