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數學幾題...

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1.) slove the following equations:10的x次方=0.012.) slove 2的x+2次方-2x次方=48.3.) after English test, John and David write an expression on the test paper to display their test marks. "^_^" represents 1, while ">_<" represents 0.john... 顯示更多 1.) slove the following equations: 10的x次方=0.01 2.) slove 2的x+2次方-2x次方=48. 3.) after English test, John and David write an expression on the test paper to display their test marks. "^_^" represents 1, while ">_<" represents 0. john 4個^_^,3個>_< david5個^_^,1個>_< A) how many marks did each get in the test in denary scale? b) who had got the highest mark? c) express twicw the difference of their marks in denary scale.

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1. 10^x = 0.01 10^x = 1/100 = 1/(10^2) = 10^(-2) x = -2 2. 2^(x+2) - 2^x = 48 2^x(2^2 - 1) = 48 2^x (3) = 48 2^x = 16 2^x = 2^4 x = 4 3. john 1111000 david 111110 A) john 2^6 + 2^5 + 2^4 + 2^3 = 64 + 32 + 16 + 8 = 120 david 2^5 + 2^4 + 2^3 + 2^2 + 2^1 = 32 + 16 + 8 +4 + 2 = 62 B) john C) Twice the difference = 2(120 - 62) = 116 = 1110100 (denary scale)

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