qr code generator visual basic 2010 Quadratic Applications in .NET framework

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CHAPTER 11 Quadratic Applications
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1 The product of two consecutive odd numbers is 399 Find the numbers 2 The product of two consecutive numbers is 380 Find the numbers 3 The product of two consecutive numbers is 650 Find the numbers 4 The product of two consecutive even numbers is 288 What are the numbers 5 Two numbers di er by 7 Their product is 228 What are the numbers
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1 Let x rst number x x 2 399 x2 2x 399 x2 2x 399 0 x 19 x 21 0 x 19 0 x 19 x 2 21 x 21 0 x 21 x 2 19 x 2 second number
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There are two solutions: 19 and 21, and 21 and 19 2 Let x rst number x x 1 380 x2 x 380 x2 x 380 0 x 20 x 19 0 x 1 second number
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x 20 0 x 20 x 1 19
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CHAPTER 11 Quadratic Applications
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x 19 0 x 19 x 1 20
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There are two solutions: 19 and 20, and 19 and 20 3 Let x rst number x x 1 650 x2 x 650 x2 x 650 0 x 25 x 26 0 x 25 0 x 25 x 1 26 x 26 0 x 26 x 1 25 x 1 second number
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There are two solutions: 25 and 26, and 25 and 26 4 Let x rst number x x 2 288 x2 2x 288 x2 2x 288 0 x 16 x 18 0 x 16 0 x 16 x 2 18 x 18 0 x 18 x 2 16 x 2 second number
There are two solutions: 16 and 18, and 16 and 18 5 Let x rst number x x 7 228 x2 7x 228 x2 7x 228 0 x 12 x 19 0 x 7 second number
CHAPTER 11 Quadratic Applications
x 12 0 x 12 x 7 19 x 19 0 x 19 x 7 12
There are two solutions: 12 and 19, 12 and 19
Revenue
A common business application of quadratic equations occurs when raising a price results in lower sales or lowering a price results in higher sales The obvious question is what to charge to bring in the most revenue This problem is addressed in Algebra II and Calculus The problem addressed here is nding a price that would bring in a particular revenue The problem involves raising (or lowering) a price by a certain number of increments and sales decreasing (or increasing) by a certain amount for each incremental change in the price For instance, suppose for each increase of $10 in the price, two customers are lost The price and sales level both depend on the number of $10 increases If the price is increased by $10, two customers are lost If the price is increased by $20, 2 2 4 customers will be lost If the price is increased by $30, 2 3 6 customers will be lost If the price does not change, 2 0 0 customers will be lost The variable will represent the number of incremental increases (or decreases) of the price The revenue formula is R PQ where R represents the revenue, P represents the price, and Q represents the number sold If the price is increased, then P will equal the current price plus the variable times the increment If the price is decreased, then P will equal the current price minus the variable times the increment If the sales level is decreased, then Q will equal the current sales level minus the variable times the incremental loss If the sales level is increased, then Q will equal the current sales level plus the variable times the incremental gain
Examples
A department store sells 20 portable stereos per week at $80 each The manager believes that for each decrease of $5 in the price, six more stereos will be sold Let x represent the number of $5 decreases in the price Then the price will decrease by 5x:
P 80 5x:
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