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# Tutor profile: Manroocha S.

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Manroocha S.
Tutor for many years, Excited to work with you! :)
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## Questions

### Subject:Basic Math

TutorMe
Question:

$$Question\ Subject: 6th\ Grade\ Math$$ $$A\ school\ has\ 90\ pencils\ to\ give\ out\ to\ it's\ students. There\ are\ 3\ classrooms\, each\ with\ 5\ students\ in\ them. How\ many\ pencils\ will\ each\ classroom\ get? How\ many\ pencils\ will\ each\ student\ get?$$

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Manroocha S.

$$The\ first\ thing\ to\ note\ here\ is\ that\ there\ are\ two\ questions\ we\ need\ to\ answer, each\ having\ their\ unique\ solution. One\ question\ is\ asking\ how\ many\ pencils\ each\ of\ the\ 3\ classrooms\ will\ get; the\ second\ question\ is\ focused\ on\ how\ many\ pencils\ each\ student\ will\ get.$$ $$Let's\ start\ with\ how\ many\ pencils\ each\ classroom\ will\ get. There\ are\ a\ total\ of\ 90\ pencils, with\ 3\ classrooms\ to\ divide\ them\ evenly\ between. Since\ we\ are\ making\ equal\ groups, we\ use\ division\ to\ help\ us\ reach\ the\ answer. We\ can\ construct\ the\ following\ equation\ model: \frac{Total\ Units}{Number\ of\ Equal\ Groups}=Number\ of\ Units\ for\ Each\ Group$$ $$Let's\ use\ the\ numbers\ we\ have\ in\ the\ problem\ to\ solve\ the\ equation\ we\ created:$$ $$\frac{90}{3}= ?$$ $$Now, we\ can\ always\ use\ multiplication\ to\ help\ us\ fill\ in\ the\ question\ mark. Since\ multiplication\ is\ the\ opposite\ of\ division\ we\ can\ rewrite\ the\ equation\ to\ get\ the\ following: 3*?=90. Using\ either\ method, we\ get\ 30\ pencils. Therefore, the\ answer\ to\ the\ first\ question\ is\ that\ each\ classroom\ will\ get\ 30\ pencils.$$ $$Now, we\ must\ zoom\ in\ and\ figure\ out\ how\ many\ pencils\ each\ student\ will\ receive. We\ can\ use\ our\ newfound\ 30\ pencils\ per\ classroom\ to\ help\ us\ with\ that. There\ are\ a\ total\ of\ 30\ pencils\, and\ we\ must\ divide\ them\ evenly\ between\ 6\ students. Our\ equation\ model\ from\ above\ gives\ us\ a\ way\ to\ plug\ in\ these\ values:$$ $$\frac{30\ pencils}{6\ students}= ? pencils\ per\ student.$$ $$We\ can\ also\ rewrite\ this\ into\ the\ multiplication\ problem\ 6 * ? = 30. This\ leads\ us\ to\ 5, or\ 5\ pencils\ that\ each\ student\ will\ receive.$$

### Subject:Calculus

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Question:

$$Calculus\space is\space a\space sector\space of\space math\space that\space pertains\space heavily\space to\space analyzing\space real\space world\space scenarios. \space Take\space a\space look\space at\space the\space equation\space below:$$ $$Say\space a\space water\space tank\space is\space being\space filled\space and\space the\space volume, in\space liters, of\space the\space water\space in\space the\space tank\space after\space t\space seconds\space is\space given\space by\space the\space linear\space function:$$ $$V^1(t )= 0.2 t^2$$ $$What\space would\space the\space instantaneous\space rate\space of\space change\space be\space at\space 4\space seconds?$$

Inactive
Manroocha S.

$$First, we\ need\ to\ look\ at\ the\ equation\ and\ think\ about\ what\ information\ it\ is\ providing\ us\ with. A\ preliminary\ look\ would\ allow\ us\ to\ see\ that\ we\ have\ an\ equation\ that\ represents\ how\ much\ water\ we\ have\ at\ a\ certain\ point. For\ example, if\ we\ wanted\ to\ see\ how\ much\ water\ we\ had\ at\ 4\ seconds, we\ would \set 4=t and\ plug\ that\ into\ our\ original\ equation. \The\ resulting\ answer\ would\ be\ V(4)=0.2 (4)^2, which\ would\ be\ equal\ to\ V(4) = 0.2 * 16, which\ would\ result\ in\ the\ final\ answer\ of\ V(4) = 3.2 liters. (Remember\ due\ to\ PEMDAS\ and\ our\ order\ of\ operations\, we\ would\ need\ to\ first\ square\ 4\ and\ then\ multiply\ that\ product\ by\ 0.2.)$$ $$However\, the\ question\ wants\ us\ to\ find\ the\ instantaneous\ rate\ of\ change\ at\ a\ certain\ point\ . It's\ important\ to\ notice\ the\ difference\ between\ the\ instantaneous\ rate\ of\ change\ and\ the\ average\ rate\ of\ change. The average\ rate\ of\ change\ would\ be\ looking\ at\ the\ original\ equation, \and\ asking\ ourself\ what\ the\ rate\ of\ change\ would\ be\ across\ the\ entire\ graph, \or\ over\ a\ particular\ interval. The\ instantaneous\ rate\ of\ change\ is\ looking\ at\ what\ the\ rate\ of\ change\ is\ at\ a\ particular\ point. We\ want\ to\ note\ the\ behavior\ of\ the\ function\ at\ a\ certain\ point, \in\ \this\ case\ at\ the\ 4th\ second, \to\ see\ what\ the\ behavior\ is\ like. Think\ of\ it\ like\ taking\ a\ snapshot\ in\ a\ moment\ of\ time: \we\ want\ to\ see\ the\ rate\ of\ change\ in\ just\ that\ snapshot, \not\ the\ entire\ graph\ or\ whole\ story.$$ $$W\e use\ the\ first\ derivative\ of\ the\ original\ equation\ to\ find\ the\ instantaneous\ rate\ of\ change\ at\ a\ certain\ point. The\ derivative\ allows\ us\ to\ measure\ the\ steepness\ of\ a\ graph\ at\ a\ certain\ point\, so\ it\ provides\ us\ with\ a\ new\ equation\ that\ can\ help\ us\ take\ these\ screenshots$$. $$Here\ is\ the\ original\ equation\: V^1(t )= 0.2 t^2$$ $$Let's\ take\ the\ derivative! V'(t)= 2 *0.2 * t ^ (2-1)$$ $$This\ is\ equal\ to\ V'(t) = 0.4 * t^1, or V'(t) = 0.4 t$$ $$If\ we\ want\ to\ find\ the\ instantaneous\ rate\ of\ change\ at\ the\ 4th\ second\, we\ plug\ in\ t=4\ into\ our\ new\ derivative.$$ $$V'(4) = 0.4 (4) = 1.6$$ $$One\ last\ thing\ to\ note\ here\ are\ the\ units\ we\ use\ for\ the\ derivative. We\aren't\ simply\ calculating\ liters\, or\ the\ amount\ of\ water\ at\ a\ particular\ point. We\ are\ now\ calculating\ the\ rate\ of\ change\ at\ the\ 4th\ second, which\ means\ our\ unit\ has\ to\ reflect\ that. To\ create\ the\ new\ unit, we\ model\ this\ rate\ of\ change\ using\ the\ vocabulary. Rate\ of\ change= [{liters}{seconds}, so\ our\ final\ answer\ would\ be\ 1.6 liters/second. This\ translated\ would\ mean\ that\ at\ the\ 4th\ second, the\ instantaneous\ rate\ of\ change\ of\ our\ water\ that\ 1.6\ liters\ are\ added\ per\ every\ second\.$$

### Subject:ACT

TutorMe
Question:

$$Question\ Subject: Understanding\ ACT\ Math\ Vocabulary$$ $$Question: The\ ACT\ Math\ section\ is\ known\ for\ centering\ around\ certain\ subject-specific\ vocabulary.Do\ your\ best\ to\ write\ the\ definition\ and\ an\ example\ of\ the\ following\ words\ to\ the\ best\ of\ your\ ability:$$ $$integer, equivalent, reciprocals, expression, equation$$

Inactive
Manroocha S.

$$integer: a\ whole\ number\, a\ number\ that\ is\ NOT\ a\ fraction. i.e: 6$$ $$equivalent: two\ expressions\ that\ are\ equal\ in\ value\ to\ each\ other. i.e: 5+5=8+2$$ $$reciprocals: two\ numbers\ (A\ and\ B)\ that\ when\ multiplied, their\ product\ is\ equal\ to\ 1. i.e,: 1/2\ and\ 2$$ $$expression: Numbers, symbols, or operations (+,-, etc)\ grouped\ together\ to\ show\ the\ value\ of\ something\ (i.e: 7+5, 2 x 3)$$ $$equation: a\ statement\ that\ the\ value\ of\ two\ mathematical\ expressions\ are\ equal. i.e: 4 + 5 = 9$$

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