Question

use the equation: $y = 15.8x + 30$ to answer questions #36-37.

1. after getting to drop barbie from the top of the stairs, students began wondering how high they could safely drop barbie if they used an entire bag of rubber bands to make her bungee cord. if an average bag contains 150 rubber bands, estimate how far, in centimeters, could barbie safely fall?
2. if barbie wanted to fall a distance of 450 cm, how many rubber bands would her bungee cord need?

Explanation:

Question 36

Step1: Identify the equation and variable

The given equation is \( y = 15.8x + 30 \), where \( x \) represents the number of rubber bands and \( y \) represents the fall distance (in cm). We know \( x = 150 \) (number of rubber bands in the bag).

Step2: Substitute \( x = 150 \) into the equation

Substitute \( x = 150 \) into \( y = 15.8x + 30 \):

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Step1: Identify the equation and variable

The equation is \( y = 15.8x + 30 \), where \( y = 450 \) (desired fall distance in cm) and we need to find \( x \) (number of rubber bands).

Step2: Solve for \( x \)

Start with \( y = 15.8x + 30 \), substitute \( y = 450 \):

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Since we can't have a fraction of a rubber band, we might round up, but typically in such cases, we calculate the exact value or round appropriately. If we consider the exact calculation: \( x=\frac{420}{15.8}\approx26.58 \), so approximately 27 rubber bands (or keep it as a decimal if allowed, but likely round to a whole number).

Answer:

2400 cm

Question 37