The horsepower, H produced by a truck engine is proportional to the cube of the truck's speed, S. Calculate the percentage increase in horsepower that is needed to double the speed.

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Initial Equation: Let's denote the initial speed of the truck as S and the initial horsepower as H. According to the problem, the horsepower is proportional to the cube of the truck's speed, which can be expressed as: H = k * S^3 where k is the constant of proportionality.New Speed and Horsepower: Now, we want to find the horsepower when the speed is doubled. Let's denote the new speed as S' and the new horsepower as H'. Since we are doubling the speed, we have: S' = 2SSubstitute New Speed: Substituting the new speed into the horsepower equation, we get: H' = k * (S')^3 H' = k * (2S)^3 H' = k * 8S^3Substitute Initial Horsepower: Since H = k * S^3, we can substitute H into the equation for H' to find the new horsepower in terms of the initial horsepower: H' = 8 * HCalculate Percentage Increase: To find the percentage increase in horsepower, we need to calculate the ratio of the increase in horsepower to the initial horsepower and then multiply by 100 to get the percentage: Percentage Increase = ((H' - H) / H) * 100Substitute H' into Formula: Substitute H' = 8H into the percentage increase formula: Percentage Increase = ((8H - H) / H) * 100 Percentage Increase = (7H / H) * 100 Percentage Increase = 7 * 100 Percentage Increase = 700%

The horsepower, $H$ produced by a truck engine is proportional to the cube of the truck's speed, $S$ . $\newline$ Calculate the percentage increase in horsepower that is needed to double the speed.

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The horsepower, H H H produced by a truck engine is proportional to the cube of the truck's speed, S S S.\newlineCalculate the percentage increase in horsepower that is needed to double the speed.

The horsepower, $H$ produced by a truck engine is proportional to the cube of the truck's speed, $S$ . $\newline$ Calculate the percentage increase in horsepower that is needed to double the speed.