Phy 201: General Physics I PCC-Cascade CampusMath Concepts WorksheetI. Solve for x in the following expressions:1) x + 2 = 8 x = ___________2) 3x - 12 = x x = ___________3) ½x2 + 14 = 16 x = ___________4) (2x2 + 4)/16 = 6 x = ___________5) 2x2 + 3x = 4 x = ___________6) 5x2 + 3y = 10 {where y = 2 } x = ___________ 7) A right triangle with its two shortest sides of length a = 3 and b = 4 is shown below. Note: and are inner angles.a) What is the length of the longest side, c?c = _________b) sin = _________c) cos = _________d) What are the values of and ? = _________ and = _________a = 3b = 4cPhy 201: General Physics I PCC-Cascade CampusMath Concepts Worksheet8) Consider the triangle shown to the right. a) If the two shortest sides of the right triangle above are a = 5 and b = 7, what is the angle, ?{solve using 2 different component methods}Method 1: = ___________Method 2: = ___________b) What are the new values for c and ?c = ___________ = ___________ 75cPhy 201: General Physics I PCC-Cascade CampusMath Concepts WorksheetIn physics, converting units from one unit system to another (especially within the Metric system) can appear daunting at first glance. However, with a little guidance, and a lot of practice, you can develop the necessary skill set to master this process.To begin, here is a simple mnemonic to guide you through the unit conversion process:1. Eliminate2. Replace3. RelateAll unit conversions, regardless of how complex they appear, involve these 3 simple steps. In the following sections, you will be stepped through the unit conversion process using these 3 words as a guide.Example: How many can 25.2 miles/hour be expressed in m/s? i.e. sm ?? hourmiles 25.2 Note: It is important to recognize that hour 1miles 25.2hourmiles2.25 Let’s breakdown the unit conversion process into 2 individual processes, miles to meters and hours to seconds:1. Eliminate – the unit(s) you begin with must be eliminated in a mathematically consistent manner. If a unit to be eliminated is a numerator unit, it must be divided out:sm ?? miles ???? hour 1miles 25.2If a unit to be eliminated is a denominator unit, it must be multiplied out:sm ?? ??hour ?? hour 1miles 25.22. Replace – the desired unit(s) you end up with must replace the original unit in a mathematically consistent manner.If a unit to replace is a numerator unit, it must be multiplied in:sm ?? miles ??m ?? hour 1miles 25.2If a unit to be eliminated is a denominator unit, it must be divided in:sm ?? s ??hour ?? hour 1miles 25.23. Relate – the units must be related to each other in some mathematical expression.Identify the relationship between the starting and final units:Phy 201: General Physics I PCC-Cascade CampusMath Concepts Worksheet1 mile = 1609 m1 hour = 3600 sTo take the guess work out of where the values should go, match the value with its corresponding unit:For the distance conversion:sm ?? mile 1m 1609 hour 1miles 25.2For the time conversion:sm ?? s 3600hour 1 hour 1miles 25.2Putting both conversions together:sm ?? s 3600hour 1 mile 1m 1609 hour 1miles 25.2Extending the Process: When the explicit relationship between the units is not known, it is often necessary to link them to a common unit (in the “Relate” phase). For example, when converting from mg to kg it is difficult to find a direct expression that relates these units. However, these units can both be related to grams (g) (by replacing theprefix with its corresponding power of 10).1 mg = 10-3 g1 kg = 103 gTherefore we can no relate mg to kg. To do so, divide the top expression by the bottom expression:6-3-310g 10g 10kg 1mg 1or 1 mg = 10-6 kgNote: the smaller unit (mg) has a larger value and the larger unit (kg) has a smaller value.Phy 201: General Physics I PCC-Cascade CampusMath Concepts WorksheetLet’s try one: How is 12.5 mg expressed in kg (i.e. 12.5 mg = ___ kg)?1. Eliminate: {assign mg units to the denominator of the conversion factor}kg ________mg ????1mg 12.52. Replace: {assign kg units to the numerator of the conversion factor}kg ________mg ??kg ??1mg 12.53. Relate: {assign the corresponding value to its unit, using 1 mg = 10-6 kg}kg 1025.11105.12mg 1kg 101mg 12.556-6xkgxNow, it’s your turn: 0.25 nm = ___ cm?1. Eliminate: cm ?? ??1nm 0.25{fill-in the blank with correct unit}2. Replace: cm ?? 1nm 0.25{fill-in both blanks with correct units}3. Relate: a) Write-out the relation between nm & m:b) Write-out the relation between cm & m:c) Divide expression (a) by expression (b):d) Solve this expression for the original unit in (a), in this case 1 nm = _____ cm:e) Now put all of the pieces together {fill-in the blanks with correct values and units then do the math }:_____________ 1nm
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