Question

Jasmine is a structural engineer. She designs the lift hill of a roller coaster that models the equation y=x³, where y is the height and x is the length from the start of the lift hill. Using this model, how far from the start of the lift hill does the ride reach a height of 343 meters?could i have an explination or a step b y stepnguide telling me how to solve??​

Answer 1

To find the distance at which Jasmine's roller coaster reaches 343 meters in height, we solve the equation y = x³ by taking the cube root of 343, which results in x = 7 meters.

Step-by-step explanation:

Jasmine, a structural engineer, is designing the lift hill of a roller coaster, and she has modeled the equation of the hill as y = x³, where y is the height and x is the length from the start of the lift hill. To find how far from the start of the lift hill the ride reaches a height of 343 meters, we can follow these steps:

1. Set the height y equal to 343 meters, which is the given height at which we want to find the length.
2. Solve the equation 343 = x³ for x.
3. Recognize that 343 is a cube number and can be expressed as 7³.
4. Therefore, the value of x that satisfies the equation is x = 7, which is the cube root of 343.

So, Jasmine's roller coaster reaches a height of 343 meters at a length of 7 meters from the start of the lift hill.