Select The Correct Answer From Each Drop-down Menu.Let $d(t)$ Be The Total Number Of Miles Joanna Has Cycled, And Let $t$ Represent The Number Of Hours Before Stopping For A Break During Her Ride.${d(t) = 12t + 20}$So,
Introduction
In this problem, we are given a linear equation that represents the total number of miles Joanna has cycled, denoted as $d(t)$, and the number of hours before stopping for a break during her ride, denoted as $t$. The equation is given by $d(t) = 12t + 20$. Our task is to select the correct answer from each drop-down menu.
Analyzing the Equation
The given equation $d(t) = 12t + 20$ represents a linear relationship between the total number of miles cycled and the number of hours before stopping for a break. Here, $d(t)$ is a function of $t$, where $t$ is the independent variable and $d(t)$ is the dependent variable.
Breaking Down the Equation
To understand the equation better, let's break it down into its components. The equation can be written as:
Here, $12t$ represents the rate at which Joanna cycles, and $20$ represents the initial number of miles she has cycled before starting her ride.
Understanding the Rate
The rate at which Joanna cycles is represented by the coefficient $12$ in the equation. This means that for every hour she cycles, she covers a distance of $12$ miles.
Understanding the Initial Distance
The initial distance covered by Joanna is represented by the constant term $20$ in the equation. This means that before starting her ride, Joanna has already cycled a distance of $20$ miles.
Selecting the Correct Answer
Now that we have analyzed the equation, let's select the correct answer from each drop-down menu.
Drop-down Menu 1: What is the rate at which Joanna cycles?
- 12 miles per hour
- 20 miles per hour
- 15 miles per hour
The correct answer is 12 miles per hour.
Drop-down Menu 2: What is the initial number of miles Joanna has cycled before starting her ride?
- 10 miles
- 20 miles
- 15 miles
The correct answer is 20 miles.
Drop-down Menu 3: What is the total number of miles Joanna has cycled after 3 hours?
- 40 miles
- 60 miles
- 50 miles
To find the total number of miles Joanna has cycled after 3 hours, we need to substitute $t = 3$ into the equation $d(t) = 12t + 20$. This gives us:
Therefore, the correct answer is 56 miles.
Drop-down Menu 4: What is the total number of miles Joanna has cycled after 5 hours?
- 80 miles
- 100 miles
- 90 miles
To find the total number of miles Joanna has cycled after 5 hours, we need to substitute $t = 5$ into the equation $d(t) = 12t + 20$. This gives us:
Therefore, the correct answer is 80 miles.
Conclusion
Frequently Asked Questions
Q: What is the equation that represents the total number of miles Joanna has cycled?
A: The equation is given by $d(t) = 12t + 20$, where $d(t)$ is the total number of miles Joanna has cycled, and $t$ represents the number of hours before stopping for a break during her ride.
Q: What is the rate at which Joanna cycles?
A: The rate at which Joanna cycles is represented by the coefficient $12$ in the equation. This means that for every hour she cycles, she covers a distance of $12$ miles.
Q: What is the initial number of miles Joanna has cycled before starting her ride?
A: The initial distance covered by Joanna is represented by the constant term $20$ in the equation. This means that before starting her ride, Joanna has already cycled a distance of $20$ miles.
Q: How do I select the correct answer from each drop-down menu?
A: To select the correct answer from each drop-down menu, you need to analyze the equation and understand the rate and initial distance. Then, you can substitute the given values into the equation to find the correct answer.
Q: What is the total number of miles Joanna has cycled after 3 hours?
A: To find the total number of miles Joanna has cycled after 3 hours, you need to substitute $t = 3$ into the equation $d(t) = 12t + 20$. This gives us:
Therefore, the correct answer is 56 miles.
Q: What is the total number of miles Joanna has cycled after 5 hours?
A: To find the total number of miles Joanna has cycled after 5 hours, you need to substitute $t = 5$ into the equation $d(t) = 12t + 20$. This gives us:
Therefore, the correct answer is 80 miles.
Q: Can I use the equation to find the total number of miles Joanna has cycled after any number of hours?
A: Yes, you can use the equation to find the total number of miles Joanna has cycled after any number of hours. Simply substitute the given value of $t$ into the equation $d(t) = 12t + 20$ to find the correct answer.
Q: What is the significance of the equation in real-life scenarios?
A: The equation can be used to model real-life scenarios where the rate of change is constant. For example, it can be used to model the growth of a population, the flow of a fluid, or the distance traveled by an object.
Conclusion
In this Q&A article, we answered frequently asked questions about the problem and the equation that represents the total number of miles Joanna has cycled. We provided step-by-step solutions to the problem and explained the significance of the equation in real-life scenarios.