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content/index.md

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content/public/001.Math/Algebra/Dimensions of Drag/Dimensions of Drag.md

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@@ -47,11 +47,11 @@ What is the dimensions of the coefficient of drag?
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Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:
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| For | Use |
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| For | Use |
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| ---- | ----|
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| $M$ | M |
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| $L$ | L |
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| $T$ | T |
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| $M$ | M |
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| $L$ | L |
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| $T$ | T |
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## Attribution
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content/public/001.Math/Algebra/Smudge/Smudge.md

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substitutions:
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params:
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vars:
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name: Lorenzo
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name: Mateo
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title: Smudge
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---
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# {{ params.vars.title }}
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{{ params.vars.name }} is writing a physics test, and their formula sheet has a smudge on it, making it hard to read the exponent of one of their equations, which describes the energy stored in a spring.
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Their copy reads $U = \frac{1}{2}kx^?$, where $?$ represents the number that they can't read.
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Rather than asking the instructor (WHICH YOU SHOULD ALWAYS DO WHEN WRITING A TEST!), {{ params.vars.name }} decides to use dimensional analysis to figure out the power.
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{{ params.vars.name }} remembers that the units of energy, $U$, are \[$U$\] = $J$ = $Nm$, the units of the spring constant, $k$, are \[$k$\] = $\frac{\text{N}}{\text{m}}$, and the units of position, $x$, are \[$x$\] = $m$, where 1 $N$ = 1 $kg$ $\frac{\text{m}}{\text{s}^2}$.
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{{ params.vars.name }} remembers that the units of energy, $U$, are [$U$] = $J$ = $Nm$, the units of the spring constant, $k$, are [$k$] = $\frac{\text{N}}{\text{m}}$, and the units of position, $x$, are [$x$] = $m$, where 1 $N$ = 1 $kg$ $\frac{\text{m}}{\text{s}^2}$.
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## Part 1
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Express the units of $U$ in terms of $kg$, $m$ and $s$.
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Note that it may not be necessary to use every variable. Use the following table as a reference for each variable.
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| For | Use |
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| For | Use |
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|----------|-------|
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| $kg$ | kg |
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| $m$ | m |
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| $s$ | s |
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| $kg$ | kg |
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| $m$ | m |
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| $s$ | s |
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### Answer Section
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Note that it may not be necessary to use every variable. Use the following table as a reference for each variable.
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| For | Use |
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| For | Use |
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|----------|-------|
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| $kg$ | kg |
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| $m$ | m |
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| $s$ | s |
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| $kg$ | kg |
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| $m$ | m |
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| $s$ | s |
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### Answer Section
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content/public/001.Math/Derivatives/Vehicle_Velocity/Vehicle_Velocity.md

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params:
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vars:
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title: Vehicle Velocity
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vehicle: car
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vehicle: sedan
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units: $m/s$
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i_1: 1
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i_1: 4
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i_2: 3
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j_1: 7
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j_2: 2
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s: 1
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s: 3
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part1:
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ans1:
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value: (-1$\hat{\imath}$ - 1$\hat{\jmath}$)
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value: (21$\hat{\imath}$ + 479/9$\hat{\jmath}$)
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ans2:
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value: (-1$\hat{\imath}$ + 6$\hat{\jmath}$)
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value: (21$\hat{\imath}$ + 54$\hat{\jmath}$)
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ans3:
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value: (-2$\hat{\imath}$ + 9$\hat{\jmath}$)
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value: (27$\hat{\imath}$ + 169/3$\hat{\jmath}$)
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ans4:
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value: (-2$\hat{\imath}$ - 1$\hat{\jmath}$)
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value: (27$\hat{\imath}$ + 479/9$\hat{\jmath}$)
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ans5:
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value: (-1$\hat{\imath}$ + 9$\hat{\jmath}$)
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value: (21$\hat{\imath}$ + 169/3$\hat{\jmath}$)
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---
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# {{ params.vars.title }}
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A {{ params.vars.vehicle }}'s position as a function of time is given by $\vec{r} =$ ({{ params.i_1 }}$t^2 -$ {{ params.i_2 }}$t)\hat{\imath} + ($ {{ params.j_1 }}$t^{-1}+$ {{ params.j_2 }} $t^3)\hat{\jmath}$ where $\vec{r}$ is in meters and $t$ is in seconds.

content/public/001.Math/Derivatives/Velocity Derivatives/velocity_derivative.md

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vars:
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title: Velocity to Acceleration
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units: $m/s^2$
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c: 1.3
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c: 0.6
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t: 2
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part1:
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ans1:
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value: 0.33
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value: 0.15
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ans2:
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value: -0.33
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value: -0.15
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ans3:
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value: -0.33
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value: -0.15
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ans4:
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value: 0.33
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value: 0.15
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ans5:
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value: The acceleration is 0
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---

content/public/001.Math/Diagnostic/math_diagnostic01/math_diagnostic01.md

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title: Math Diagnostic01
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part1:
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ans1:
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value: 2.3E46
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value: 9.6E30
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ans2:
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value: 4.5E7
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value: 4.3E4
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ans3:
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value: 8731.800418368457
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value: 4221.521560096523
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ans4:
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value: '4.2E-83'
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value: '6.9E-22'
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ans5:
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value: Don't Know
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---

content/public/001.Math/Diagnostic/math_diagnostic02/math_diagnostic02.md

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params:
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vars:
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title: Math Diagnostic02
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x: 541.9998137
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sf: 5
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x: 175.45251986
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sf: 6
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part1:
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ans1:
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value: 542.0
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value: 175.453
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ans2:
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value: 542.1
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value: 175.553
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ans3:
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value: 541.99981
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value: 175.45252
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ans4:
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value: 532.0
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value: 165.453
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---
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# {{ params.vars.title }}
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content/public/001.Math/Diagnostic/math_diagnostic03/math_diagnostic03.md

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params:
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title: Math Diagnostic03
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formula: 8x + -7 > -4x + 10
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formula: -2x + -3 > -6x + 6
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part1:
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ans1:
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value: x > 17/12
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value: x > 9/4
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ans2:
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value: x < 17/12
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value: x < 9/4
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ans3:
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value: x < 12/17
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value: x < 4/9
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ans4:
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value: x > 12/17
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value: x > 4/9
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ans5:
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value: Don't Know
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---

content/public/001.Math/Diagnostic/math_diagnostic05/math_diagnostic05.md

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title: Math Diagnostic05
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expr: $\dfrac{x}{2}$
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num2: 9
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num3: 10
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expr: $\dfrac{x}{4}$
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num2: 2
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num3: 2
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part1:
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ans1:
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value: 180
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value: 16
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ans2:
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value: 9/2
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value: 1/2
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ans3:
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value: 20
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value: 8
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ans4:
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value: '45'
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value: '1'
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ans5:
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value: Don't Know
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---

content/public/001.Math/Diagnostic/math_diagnostic06/math_diagnostic06.md

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params:
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vars:
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title: Math Diagnostic06
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eq: $\dfrac{x-1}{x-5}$ = $ \dfrac{x+2}{x+9}$
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eq: $\dfrac{x-2}{x-8}$ = $ \dfrac{x+3}{x+9}$
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part1:
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ans1:
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value: -43/17
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value: '-3'
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ans2:
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value: -1/11
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value: -1/2
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ans3:
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value: 43/5
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value: '33'
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ans4:
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value: 13/17
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value: 1/2
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ans5:
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value: -23/7
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value: -43/6
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ans6:
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value: None of the above
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---

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