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Value added tax (VAT) is charged as a percentage of the price of a product or service. So the first thing we need to know is how to calculate a percentage. The way I like to think of percentages is to break up the word into “per” and “cent”. And since “cent” is short for “century” (think a hundred in years and cricket), percent means “per hundred”. The current VAT rate is 15% – 15 per hundred – meaning you pay R15 of VAT per R100 of cost. For something that costs R100 excluding VAT, we just need to add the R15 VAT to the price, giving us a total of R115 including VAT. To calculate the VAT payable on any amount, it helps to remember that VAT is charged as a percentage “of” the purchase price. And in maths, the word “of” simply means to multiply. To calculate the VAT (15%) of something that costs R25 means we need to multiply R25 by 15%. And since we now know that 15% is just (15/100) we can multiply it by R25. Like this: To get the total cost including VAT, we add the VAT...

Optimized -6 min https://www. mathsisfun.com /algebra/completing-square.html View original Completing the Square " Completing the Square " is where we ... ... take a  Quadratic Equation like this: and turn it into this: ax 2  + bx + c = 0 a(x+ d ) 2  +  e  = 0 For those of you in a hurry, I can tell you that: d =  b 2a and: e = c − b 2 4a But if you have time, let me show you how to " Complete the Square " yourself. Completing the Square Say we have a simple expression like  x 2  + bx . Having  x twice in the same expression can make life hard. What can we do? Well, with a little inspiration from Geometry we can convert it, like this: As you can see  x 2  + bx  can be rearranged  nearly  into a square ... ... and we can  complete the square  with  (b/2) 2 In Algebra it looks like this: x 2  + bx + (b/2)...

       Online Notes   Home   /  Calculus III   /  Multiple Integrals   / Double Integrals Notes   Practice   Assignment Hide Mobile Notice      MOBILE NOTICE You appear to be on a device with a "narrow" screen width ( i.e.  you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see qthem) and some of the menu items will be cutto the narrow screen width. Section 4-1 : Double Integrals Before starting on double integrals let’s do a quick review of the definition of definite integrals for functions of single variables. First, when working with the integral, ∫ b a f ( x ) d x ∫ a b f ( x ) d x we think of  x x ’s as coming from the interval  a ≤ x ≤ b a ≤ x ≤ b . For these integra...