polyhymnio
polyhymnio
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L = 2W – 3 L + W = 3W – 3 = 21 3W = 24 W = 8 L = 13
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4sin(x)cos(x)
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Multiply left side by (cosh2x + sinh2x)/(cosh2x + sinh2x) (cosh2x + sinh2x)/[(cosh2x + sinh2x)(cosh2x – sinh2x)] = (cosh2x + sinh2x)/(cosh²2x – sinh²2x) = cosh2x + sinh2x
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Multiply left side by (cosh2x + sinh2x)/(cosh2x + sinh2x) (cosh2x + sinh2x)/[(cosh2x + sinh2x)(cosh2x – sinh2x)] = (cosh2x + sinh2x)/(cosh²2x – sinh²2x) = cosh2x + sinh2x
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Use the rational root theorem and synthetic division
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Use the rational root theorem and synthetic division
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cos(2x) = 2cos²(x) - 1 sin(2x) = 2sin(x)cos(x) (1 + 2cos²(x) - 1)/(2sin(x)cos(x)) = cos²(x)/(sin(x)cos(x)) = cos(x)/sin(x) = cot(x)
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Multiply by 60 minutes/hour. Be sure to carry your units so the minutes cancel, or you may end up dividing instead!
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a. x(x + 3i)(x – 3i) = 0, x = 0, ±3i b. ((x – 2) + 2)² = x² = 0, x = 0
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a. x(x + 3i)(x – 3i) = 0, x = 0, ±3i b. ((x – 2) + 2)² = x² = 0, x = 0
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cos(3x) = cos(2x + x) = cos(2x)cos(x) – sin(2x)sin(x) = (2cos²x – 1)(cosx) – 2sinx cosx sinx = cosx[(2cos²x – 1) – 2(1 – cos²x)] = 2cos³x – cosx – 2cosx + 2cos³x = 4cos³x – 3cosx QED
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There are infinitely many Pythagorean triples. True. Example: 500² = 300² + 400²
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Let s = number of 6-cent stamps and f = number of 15-cent stamps f = 4s 0.06s + 0.15f = 0.06s + 0.15(4s) = 0.66s = 165 s = 165/0.66 = 250 6-cent stamps f = 4s = 1000 15-cent stamps Check: 1000*$0.15 + 250*$0.06 = $165
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Let s = number of 6-cent stamps and f = number of 15-cent stamps f = 4s 0.06s + 0.15f = 0.06s + 0.15(4s) = 0.66s = 165 s = 165/0.66 = 250 6-cent stamps f = 4s = 1000 15-cent stamps Check: 1000*$0.15 + 250*$0.06 = $165
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The GCF of the left side is y, so y(y – 4) = 0 with solutions y = 0, 4
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The GCF of the left side is y, so y(y – 4) = 0 with solutions y = 0, 4
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Let s = number of 6-cent stamps and f = number of 15-cent stamps f = 4s 0.06s + 0.15f = 0.06s + 0.15(4s) = 0.66s = 165 s = 165/0.66 = 250 6-cent stamps f = 4s = 1000 15-cent stamps Check: 1000*$0.15 + 250*$0.06 = $165
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There are infinitely many Pythagorean triples. True. Example: 500² = 300² + 400²
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cos(3x) = cos(2x + x) = cos(2x)cos(x) – sin(2x)sin(x) = (2cos²x – 1)(cosx) – 2sinx cosx sinx = cosx[(2cos²x – 1) – 2(1 – cos²x)] = 2cos³x – cosx – 2cosx + 2cos³x = 4cos³x – 3cosx QED
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a. x(x + 3i)(x – 3i) = 0, x = 0, ±3i b. ((x – 2) + 2)² = x² = 0, x = 0
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a. x(x + 3i)(x – 3i) = 0, x = 0, ±3i b. ((x – 2) + 2)² = x² = 0, x = 0
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Multiply by 60 minutes/hour. Be sure to carry your units so the minutes cancel, or you may end up dividing instead!
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Multiply by 60 minutes/hour. Be sure to carry your units so the minutes cancel, or you may end up dividing instead!
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cos(2x) = 2cos²(x) - 1 sin(2x) = 2sin(x)cos(x) (1 + 2cos²(x) - 1)/(2sin(x)cos(x)) = cos²(x)/(sin(x)cos(x)) = cos(x)/sin(x) = cot(x)
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Use the rational root theorem and synthetic division
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4sin(x)cos(x)