Max Rides His Scooter Toward Kim And Then Passes Her At A Constant Speed. His Distance In Feet, D D D , From Kim T T T Seconds After He Started Riding His Scooter Is Given By D = ∣ 150 − 9 T ∣ D=|150-9t| D = ∣150 − 9 T ∣ .1. What Does The 150 In The Equation

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Introduction

In this article, we will delve into the world of mathematics and explore the concept of distance equations. We will use the scenario of Max riding his scooter towards Kim and passing her at a constant speed to understand the significance of the equation d=∣150−9t∣d=|150-9t|. This equation represents the distance in feet, dd, from Kim tt seconds after Max started riding his scooter.

The Significance of the 150 in the Equation

The equation d=∣150−9t∣d=|150-9t| represents the distance between Max and Kim at any given time tt. The number 150 in the equation is crucial in understanding the initial position of Max relative to Kim. In this context, the 150 represents the initial distance between Max and Kim in feet.

Breaking Down the Equation

To understand the significance of the 150, let's break down the equation d=∣150−9t∣d=|150-9t|. The absolute value function ∣x∣|x| represents the distance of xx from 0 on the number line. In this case, the absolute value function is used to ensure that the distance dd is always non-negative.

The equation d=∣150−9t∣d=|150-9t| can be rewritten as:

  • d=150−9td = 150 - 9t when 150−9t≥0150 - 9t \geq 0
  • d=9t−150d = 9t - 150 when 150−9t<0150 - 9t < 0

Interpreting the Equation

When 150−9t≥0150 - 9t \geq 0, the equation d=150−9td = 150 - 9t represents the distance between Max and Kim as Max is moving away from Kim. In this case, the 150 represents the initial distance between Max and Kim.

When 150−9t<0150 - 9t < 0, the equation d=9t−150d = 9t - 150 represents the distance between Max and Kim as Max is moving towards Kim. In this case, the 150 represents the initial distance between Max and Kim, but in the opposite direction.

Conclusion

In conclusion, the 150 in the equation d=∣150−9t∣d=|150-9t| represents the initial distance between Max and Kim in feet. The equation is a representation of the distance between Max and Kim at any given time tt, and the 150 is a crucial component in understanding the initial position of Max relative to Kim.

Max's Scooter Ride: A Mathematical Analysis

Introduction

In this section, we will analyze Max's scooter ride using the equation d=∣150−9t∣d=|150-9t|. We will explore the concept of distance equations and how they can be used to model real-world scenarios.

The Distance Equation

The equation d=∣150−9t∣d=|150-9t| represents the distance in feet, dd, from Kim tt seconds after Max started riding his scooter. The equation is a representation of the distance between Max and Kim at any given time tt.

Graphing the Equation

To visualize the equation, we can graph it on a coordinate plane. The x-axis represents time tt in seconds, and the y-axis represents the distance dd in feet.

import numpy as np
import matplotlib.pyplot as plt

t = np.linspace(0, 20, 400)
d = np.abs(150 - 9*t)


plt.plot(t, d)
plt.xlabel('Time (s)')
plt.ylabel('Distance (ft)')
plt.title('Distance Equation')
plt.grid(True)
plt.show()

Interpreting the Graph

The graph represents the distance between Max and Kim at any given time tt. The graph shows that the distance between Max and Kim decreases as Max approaches Kim.

Conclusion

In conclusion, the equation d=∣150−9t∣d=|150-9t| represents the distance between Max and Kim at any given time tt. The graph of the equation shows that the distance between Max and Kim decreases as Max approaches Kim.

Max's Scooter Ride: A Real-World Application

Introduction

In this section, we will explore the real-world application of Max's scooter ride. We will analyze the equation d=∣150−9t∣d=|150-9t| and how it can be used to model real-world scenarios.

The Real-World Application

The equation d=∣150−9t∣d=|150-9t| can be used to model real-world scenarios such as:

  • A car traveling at a constant speed towards a stationary object
  • A person walking towards a stationary object
  • A ball rolling towards a stationary object

Conclusion

In conclusion, the equation d=∣150−9t∣d=|150-9t| represents the distance between Max and Kim at any given time tt. The equation can be used to model real-world scenarios such as a car traveling at a constant speed towards a stationary object, a person walking towards a stationary object, and a ball rolling towards a stationary object.

Max's Scooter Ride: A Mathematical Model

Introduction

In this section, we will explore the mathematical model of Max's scooter ride. We will analyze the equation d=∣150−9t∣d=|150-9t| and how it can be used to model real-world scenarios.

The Mathematical Model

The equation d=∣150−9t∣d=|150-9t| can be used to model real-world scenarios such as:

  • A car traveling at a constant speed towards a stationary object
  • A person walking towards a stationary object
  • A ball rolling towards a stationary object

Conclusion

In conclusion, the equation d=∣150−9t∣d=|150-9t| represents the distance between Max and Kim at any given time tt. The equation can be used to model real-world scenarios such as a car traveling at a constant speed towards a stationary object, a person walking towards a stationary object, and a ball rolling towards a stationary object.

Max's Scooter Ride: A Conclusion

Introduction

In this article, we have explored the concept of distance equations and how they can be used to model real-world scenarios. We have analyzed the equation d=∣150−9t∣d=|150-9t| and how it can be used to model Max's scooter ride.

Conclusion

Introduction

In this article, we will answer some of the most frequently asked questions about Max's scooter ride and the equation d=∣150−9t∣d=|150-9t|. We will explore the concept of distance equations and how they can be used to model real-world scenarios.

Q: What is the equation d=∣150−9t∣d=|150-9t| used to model?

A: The equation d=∣150−9t∣d=|150-9t| is used to model the distance between Max and Kim at any given time tt. It represents the distance in feet, dd, from Kim tt seconds after Max started riding his scooter.

Q: What is the significance of the 150 in the equation?

A: The 150 in the equation represents the initial distance between Max and Kim in feet. It is a crucial component in understanding the initial position of Max relative to Kim.

Q: What happens when 150−9t≥0150 - 9t \geq 0?

A: When 150−9t≥0150 - 9t \geq 0, the equation d=150−9td = 150 - 9t represents the distance between Max and Kim as Max is moving away from Kim.

Q: What happens when 150−9t<0150 - 9t < 0?

A: When 150−9t<0150 - 9t < 0, the equation d=9t−150d = 9t - 150 represents the distance between Max and Kim as Max is moving towards Kim.

Q: Can the equation d=∣150−9t∣d=|150-9t| be used to model other real-world scenarios?

A: Yes, the equation d=∣150−9t∣d=|150-9t| can be used to model other real-world scenarios such as:

  • A car traveling at a constant speed towards a stationary object
  • A person walking towards a stationary object
  • A ball rolling towards a stationary object

Q: How can the equation d=∣150−9t∣d=|150-9t| be graphed?

A: The equation d=∣150−9t∣d=|150-9t| can be graphed on a coordinate plane using the x-axis to represent time tt in seconds and the y-axis to represent the distance dd in feet.

Q: What is the significance of the graph of the equation d=∣150−9t∣d=|150-9t|?

A: The graph of the equation d=∣150−9t∣d=|150-9t| represents the distance between Max and Kim at any given time tt. It shows that the distance between Max and Kim decreases as Max approaches Kim.

Q: Can the equation d=∣150−9t∣d=|150-9t| be used to model other mathematical concepts?

A: Yes, the equation d=∣150−9t∣d=|150-9t| can be used to model other mathematical concepts such as:

  • Linear equations
  • Quadratic equations
  • Absolute value equations

Q: How can the equation d=∣150−9t∣d=|150-9t| be used in real-world applications?

A: The equation d=∣150−9t∣d=|150-9t| can be used in real-world applications such as:

  • Modeling the distance between two objects in motion
  • Calculating the time it takes for an object to travel a certain distance
  • Determining the speed of an object

Conclusion

In conclusion, the equation d=∣150−9t∣d=|150-9t| represents the distance between Max and Kim at any given time tt. It can be used to model real-world scenarios such as a car traveling at a constant speed towards a stationary object, a person walking towards a stationary object, and a ball rolling towards a stationary object. The equation can also be used to model other mathematical concepts and real-world applications.