One Of The Lamp Posts At A Bank Has A Motion Detector On It, And The Equation \[$(x+15)^2+(y-12)^2=25\$\] Describes The Boundary Within Which Motion Can Be Sensed.What Is The Greatest Distance, In Feet, A Person Could Be From The Lamp And Be
Introduction
In a typical bank setting, security is a top priority. One of the ways to enhance security is by installing motion detectors around the premises. These detectors can be placed on lamp posts, walls, or even ceilings, and they work by sensing any movement within a certain boundary. The equation {(x+15)2+(y-12)2=25$}$ describes the boundary within which motion can be sensed. In this article, we will delve into the meaning of this equation and determine the greatest distance a person could be from the lamp post and still be detected.
Understanding the Equation
The equation {(x+15)2+(y-12)2=25$}$ represents a circle with a center at and a radius of 5. This means that the motion detector can sense any movement within a 5-foot radius of the lamp post. To understand this, let's break down the equation:
- The term represents the horizontal distance from the center of the circle (the lamp post) to any point on the circle.
- The term represents the vertical distance from the center of the circle to any point on the circle.
- The on the right-hand side of the equation represents the square of the radius of the circle.
Visualizing the Circle
To better understand the equation, let's visualize the circle. We can do this by plotting the center of the circle, , and then drawing a circle with a radius of 5 around it. This will give us a visual representation of the boundary within which motion can be sensed.
Determining the Greatest Distance
Now that we have a visual representation of the circle, we can determine the greatest distance a person could be from the lamp post and still be detected. This distance will be equal to the radius of the circle, which is 5 feet. Therefore, the greatest distance a person could be from the lamp post and still be detected is 5 feet.
Conclusion
In conclusion, the equation {(x+15)2+(y-12)2=25$}$ describes the boundary within which motion can be sensed by a motion detector on a lamp post. By understanding the equation and visualizing the circle, we can determine the greatest distance a person could be from the lamp post and still be detected, which is 5 feet.
Frequently Asked Questions
Q: What is the center of the circle?
A: The center of the circle is .
Q: What is the radius of the circle?
A: The radius of the circle is 5 feet.
Q: What is the greatest distance a person could be from the lamp post and still be detected?
A: The greatest distance a person could be from the lamp post and still be detected is 5 feet.
Additional Resources
For more information on motion detectors and their applications, please refer to the following resources:
References
Final Thoughts
In conclusion, the equation {(x+15)2+(y-12)2=25$}$ describes the boundary within which motion can be sensed by a motion detector on a lamp post. By understanding the equation and visualizing the circle, we can determine the greatest distance a person could be from the lamp post and still be detected, which is 5 feet. This information can be useful for security personnel and individuals who want to understand how motion detectors work.
Introduction
In our previous article, we explored the equation {(x+15)2+(y-12)2=25$}$ and determined that it describes the boundary within which motion can be sensed by a motion detector on a lamp post. In this article, we will answer some frequently asked questions related to the motion detector equation and provide additional information to help you better understand the concept.
Q&A
Q: What is the purpose of a motion detector?
A: The purpose of a motion detector is to sense any movement within a certain boundary and trigger an alarm or alert security personnel.
Q: How does a motion detector work?
A: A motion detector works by using sensors to detect any movement within a certain range. When movement is detected, the sensor sends a signal to a control unit, which triggers an alarm or alerts security personnel.
Q: What is the difference between a motion detector and a security camera?
A: A motion detector is a device that senses movement within a certain range, while a security camera is a device that captures video footage of a scene. While both devices can be used for security purposes, they serve different functions.
Q: Can a motion detector be used in conjunction with a security camera?
A: Yes, a motion detector can be used in conjunction with a security camera. When a motion detector detects movement, it can trigger the security camera to start recording video footage.
Q: How accurate is a motion detector?
A: The accuracy of a motion detector depends on the type of sensor used and the sensitivity of the device. Some motion detectors can detect movement as small as 1-2 feet, while others may detect movement as large as 10-20 feet.
Q: Can a motion detector be used outdoors?
A: Yes, a motion detector can be used outdoors. However, it's essential to choose a device that is specifically designed for outdoor use and can withstand the elements.
Q: How often should a motion detector be tested?
A: A motion detector should be tested regularly to ensure it's functioning correctly. This can be done by simulating movement within the detection range and verifying that the device triggers an alarm or alerts security personnel.
Q: Can a motion detector be hacked?
A: Yes, a motion detector can be hacked if it's not properly secured. It's essential to choose a device with robust security features and to follow best practices for securing the device and its associated network.
Additional Resources
For more information on motion detectors and their applications, please refer to the following resources:
References
Final Thoughts
In conclusion, the equation {(x+15)2+(y-12)2=25$}$ describes the boundary within which motion can be sensed by a motion detector on a lamp post. By understanding the equation and visualizing the circle, we can determine the greatest distance a person could be from the lamp post and still be detected, which is 5 feet. This information can be useful for security personnel and individuals who want to understand how motion detectors work.
Common Misconceptions
Misconception 1: Motion detectors can detect movement from any direction.
A: While motion detectors can detect movement from multiple directions, they are typically designed to detect movement within a specific range and may not be able to detect movement from all directions.
Misconception 2: Motion detectors are 100% accurate.
A: While motion detectors can be highly accurate, they are not 100% accurate. They may detect false positives or false negatives, depending on the type of sensor used and the sensitivity of the device.
Misconception 3: Motion detectors are only used for security purposes.
A: While motion detectors are often used for security purposes, they can also be used for other purposes, such as detecting movement in a home or office to conserve energy or to monitor wildlife.
Conclusion
In conclusion, the equation {(x+15)2+(y-12)2=25$}$ describes the boundary within which motion can be sensed by a motion detector on a lamp post. By understanding the equation and visualizing the circle, we can determine the greatest distance a person could be from the lamp post and still be detected, which is 5 feet. This information can be useful for security personnel and individuals who want to understand how motion detectors work.