QUESTION 3 The propagation of uncertainty formula for the equation y - mx •b is y (AYm) + (Ay)² + (Ayp)² where Aym = (mx + b) - ((m+ Sm)x + b). Ay, = (mx + b) - (m(x + 8x) + b) and Ayn = (mx + b) – (mx + (b + Sb)). The values Sm, Sx and Sb are the uncertainties on m. x and brespectively. If m- 45+/-08. x- -14/-04 and b--33/-05 then what is the uncertainty on y? 15213
Unitary Method
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![**Question 3**
The propagation of uncertainty formula for the equation \(y = mx + b\) is:
\[
\sqrt{(\Delta y_m)^2 + (\Delta y_x)^2 + (\Delta y_b)^2}
\]
where:
- \(\Delta y_m = (mx + b) - ((m + \delta m)x + b)\)
- \(\Delta y_x = (mx + b) - (m(x + \delta x) + b)\)
- \(\Delta y_b = (mx + b) - (mx + (b + \delta b))\)
The values \(\delta m\), \(\delta x\), and \(\delta b\) are the uncertainties on \(m\), \(x\), and \(b\) respectively.
If \(m = 4.5 \pm 0.8\), \(x = -14 \pm 0.4\), and \(b = -33 \pm 0.5\), then what is the uncertainty on \(y\)?
**Answer: 1.5213**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc96294a-6867-4c53-8945-7b1c26d22cf9%2F0401cb42-7c96-4c97-9d6e-2a537a68a0b3%2F2ezzpgj_processed.jpeg&w=3840&q=75)
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