Math topic中文

Newly defined operations

Evaluate expressions under an operation rule defined in the problem itself; understand that a symbol just names a rule.

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Mixed operations with integers

Practice questions

  1. 1Consider these two operations: a⧫b=a2−b2a \blacklozenge b = a^2 - b^2, a⋆b=(a−b)2a \star b = (a - b)^2 What is the value of (5⧫3)⋆6(5 \blacklozenge 3) \star 6…
  2. 2定义：若一个整数能表示成a2+b2(a,ba^{2}+b^{2}(a,b是正整数))的形式，则称这个数为“完美数”． 例如：因为13=32+2213=3^{2}+2^{2}，所以1313是“完美数”； 再如：因为a2+2ab+2b2=(a+b)2+b2a^{2}+2ab+2b^{2}=(a+b)^{2}+b^{2}…
  3. 3The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What…
  4. 4Wind chill is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be foun…
  5. 5现定义运算a⊗b=a（1-b），则a⊗（b+1）= ，a⊗b-b⊗a= ．
  6. 6Suppose that a∗ba * b means 3a−b3a - b. What is the value of xx if 2∗(5∗x)=12 * (5 * x) = 1 A. 110\frac{1}{10} B. 2 C. 103\frac{10}{3}…