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phys: misc improvements and fixes condensed #12

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eggy merged 5 commits from physics-soup into master 2020-09-24 21:07:29 -04:00
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docs/sph3u7.md
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@ -100,10 +100,7 @@ The order of magnitude of a number can be found by converting it to scientific n
### Uncertainties
Uncertainties are stated in the form of [value] ± [uncertainty]. A value is only as precise as its absolute uncertainty. Absolute uncertainty of a **measurement** is usually represented to only 1 significant digit.
!!! note
Variables with uncertainty use an uppercase delta for their uncertainty value: $a ± \Delta a$
Uncertainties are stated in the form of $a±\Delta a$. A value is only as precise as its absolute uncertainty. Absolute uncertainty of a **measurement** is usually represented to only 1 significant digit.
- The absolute uncertainty of a number is written in the same unit as the value.
- The percentage uncertainty of a number is the written as a percentage of the value.
@ -126,13 +123,10 @@ See [Dealing with Uncertainties](/resources/g11/physics-uncertainties.pdf) for h
### Error bars
Error bars represent the uncertainty of the data, typically representing that data point's standard deviation, and can be both horizontal or vertical.
Error bars represent the uncertainty of the data, typically representing that data point's standard deviation, and can be both horizontal or vertical. A data point with uncertain values is written as $(x ± \Delta x, y ± \Delta y)$
<img src="/resources/images/error-bars.png" width=600>(Source: Kognity)</img>
!!! note
On a graph, a data point with uncertain values is written as $(x ± \Delta x, y ± \Delta y)$
### Uncertainty of gradient and intercepts
!!! note "Definition"
@ -189,7 +183,7 @@ Alternatively, for any number of vectors, negate the vector(s) being subtracted
### Adding/subtracting vectors algebraically
Vectors can be broken up into two vectors (**"components"**) laying on the x- and y-axes via trigonometry such that the resultant of the two components is the original vector. This is especially helpful when adding larger (3+) numbers of vectors.
Vectors can be broken up into two **component vectors** laying on the x- and y-axes via trigonometry such that the resultant of the two components is the original vector. This is especially helpful when adding larger (3+) numbers of vectors.
$$\vec{F}_x + \vec{F}_y = \vec{F}$$
!!! info "Reminder"