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sveticcg [70]
3 years ago
13

What is the constant of proportionality in the equation y=5/4 x

Mathematics
1 answer:
Phoenix [80]3 years ago
8 0
The COP( constant of proportionality) is the k, being multiplied by the x. In this case, it is 5/4.
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You're trying to find constants a_0,a_1,a_2 such that \hat y=a_0+a_1\hat x+a_2{\hat x}^2. Equivalently, you're looking for the least-square solution to the following matrix equation.


\underbrace{\begin{bmatrix}1&6&6^2\\1&3&3^2\\\vdots&\vdots&\vdots\\1&9&9^2\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}100\\110\\\vdots\\70\end{bmatrix}}_{\mathbf b}

To solve \mathbf{Ax}=\mathbf b, multiply both sides by the transpose of \mathbf A, which introduces an invertible square matrix on the LHS.

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Computing this, you'd find that

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3 years ago
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