Unknown Operations

Algebra Level 2

An operation exists where a ⊗ b = a b ( a + b ) a \otimes b = ab(a+b) . If a = 10 a = 10 and b = 20 b = 20 , what does 8800 ( a b ) ⊗ b \dfrac{8800}{(ab) \otimes b} equal?

28 32 0.01 0.08

Xin Ze Cai by Xin Ze Cai , 16, Australia

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2 solutions

Chew-Seong Cheong
Aug 18, 2019

8800 a b ⊗ b = 8800 200 ⊗ 20 = 8800 4000 ( 220 ) = 1 100 = 0.01 \dfrac {8800}{ab \otimes b} = \dfrac {8800}{200 \otimes 20} = \dfrac {8800}{4000(220)} = \dfrac 1{100} = \boxed{0.01} .

1 Helpful 1 Interesting 1 Brilliant 0 Confused

a_ ⊗ b_ := a b ( a + b ) \text{a\_}\otimes \text{b\_}\text{ := }a\,b\,(a+b)

8800 ( a b ) ⊗ b /. { a → 10 , b → 20 } ⇒ 1 100 \frac{8800}{(a\,b)\otimes b}\text{ /. }\, \{a\to 10,b\to 20\} \Rightarrow \frac1{100}

1 Helpful 1 Interesting 1 Brilliant 0 Confused

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