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Geometric / Ray Optics for light with wavelength is much smaller than the object sizes. Wave Theory applies when they are of similar magnitudes...

Document 261k

Geometric / Ray Optics for light with wavelength is much smaller than the object sizes. Wave Theory applies when they are of similar magnitudes...

Document 260k

Summary of Fluid Statics and Dynamics covering Pascal's Law and Principle, Archimedes Buoyancy, Laplace & Toricelli's Laws, and Bernoulli's...

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This is a compendium of my Physics Summary Sheets to help my students review the essential ideas and thus make it easy to obtain retention...

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This file covers the basic ideas a HS Student of Math should know. There are 49 ideas each of which is important in having a full grasp...

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This file outlines in an organized way the various topics and ideas in Calc 1 & 2. It is best rendered in a non Adobe PDF Reader. I...

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This table combines what most texts have as two separate pages. I have combined them because it makes it easier for the student to see relationships...

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This is a summary of the ideas in Calc 1 & 2. It is in pdf format but renders best on a non Adobe PDF Reader.

Assuming the same growth rate = 2.5% per year f(x) = Population f(x) = 6 (1.025)^x 12 = 6 (1.025)^x 2 = (1.025)^x Log 2 = Log (1.025)^x Log 2 = x Log (1.025) Power Rule for Logarithms x = Log 2 / Log (1.025) = 0.3010 / .0107 = 28.1 ...

x + y = - 116 x - y = - 52 Add the equations to eliminate y 2x = - 168 x = - 84 Plug back in to x + y = - 116 so y = -32 Check -84 - (-32) = - 52 checks ok !

There is a rational zero test. All rational solutions to f(x) = 0 will be contained in the set of ± r / ± s where r = the factors of the coefficient xn = the highest power term s = the factors of the coefficient of x0 = the constant term For f (x)= 2x^3-4x^2+5x-3 ...

x - y = 10 and x + 2y/3 = 16 Subtract - 5y/3 = - 6 y = 18/5 => x = 16 - 2/3 (18/5) = 204/15 ==>So x , y = 54/15 , 204/15 <== Check (204 - 54)/15 = 150/15 = 10

the population of purple martins p the population of raccoons, r p(r)= 750 - 3.75r the mosquito population m m (p) = 50,000 -45p. So if r = 0 then p(0) = 750 m(p) = m(750) = 50,000 - 45 (750) m = 16,250

Laws of Motion related doubt (answer)

Invoke Conservation of Energy ..... Change in PE + Change in KE = 0 .... dPE = dKE d=delta or change 1. The half of the chain off the table falls a distance L/2. It's change in potential energy dPE is rho (L/2) g (L/2) Note; [PE = mgh; rho L =...

Rates are $85 and $120 Rate x Time = $ charged 1st r 15 15 r 2nd 205 - r ...

Algebra 2 - Please Help! (answer)

Ages now 15 and 43 E + F = 58 2 (E+13) = F+13 2E + 26 = F + 13 2E - F = - 13 E + F = 58 Adding these equations eliminates F 3E = 45 E = 15 thus if E+F=58 then F=43 Checking 43+13=56 15+13=28 checks...

Algebra 2 Please Help! (answer)

$4500 at 3% & $7500 at 8% Total interest = $735 Let N(3) = Amt after 1 yr of the 3% investment of P Let N(8) = Amt after 1 yr of the 8% investment of P + $3000 N(3) + N(8) = P + (P+3000) + 735 = 2P + 3735 N(3)...

Differential Equations (answer)

A model is a replica of something original or real For example, architects build out of cardboard, small models of a proposed building. An equation, differential, integral, quadratic or even just linear, models the natural world in some respect. For example again y = x2 models...

How to calculate stopping distance? (answer)

My method is nearly identical to Arturo O. Suvat formula v2 - u2 = 2 a s v = final velocity u = initial velocity s = distance This assumes constant acceleration/deceleration So .... 0 - u2 = 2 a s The...

Go to www.khanacademy.com You can learn any one of 100 subjects with their videos, including Math, Physics, Biology, Chemistry, etc. Its just like having your own private tutor. If you need more help, message me here at WyzAnt.com Good luck !

So the data are 6 14 15 22 23 23 28 34 Mode is 23 Median 22.5 Mean 165 / 8 = 20.625