Superheroes fighting with maths
Electro and Spider-Man ( Spidey! ) are going to fight! This being a maths problem,we'll skip the specifics of this but we do know that both Electro and Spider-Man have a health of units.Also, Electro can take away units of health per second with his electro-powers.That means Spider-Man will have to defeat Electro in 10 seconds! Luckily, Spider-Man is extremely fast and he can strike Electro times ( I know it's not possible, but this is calculus ) in 10 seconds but he will lose of his striking power every time ( in other words, every attack is as strong as the last and takes away only as many units of health ).What is the minimum initial striking power Spider-Man must have ( in units of health ) to be able to defeat Electro?
The answer is 450.
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1 solution
Let Spider-Man's initial striking power be x .Every time he strikes,he has only 0 . 1 times the power of the last strike.So the total damage is x + 0 . 1 x + 0 . 0 1 x + 0 . 0 0 1 x . . . . = 1 . 1 1 1 1 1 1 1 1 . . . . . . . x = 9 1 0 x As the total damage must be ≥ 5 0 0 ,we get 5 0 0 ≤ 9 1 0 x Then,we multiply both sides by 9 to get 4 5 0 0 ≤ 1 0 x Finally, divide by 10 to get 4 5 0 ≤ x So,our answer is 4 5 0 .