The amount of time in seconds it takes for a swimmer to hear a single, hand-held, starting signal is given by the formula below, where (x,y) is the location of the starter (in meters), (0.p) is the location of the swimmer (in meters), and C is the air temperature (in degrees Celsius). Assume that the starter is located at the point (4,-2). Answer parts a and b below. √√x² + (y-p)² t(x,y.p.C)= 331.45+0.6C a. Calculate t(4, -2,30,20) and t(4, -2,20,20). Could the difference in time change the outcome of a race? t(4, -2,30,20) = (Round to five decimal places as needed.) Ay p Swimmer Starter (4,-2)
The amount of time in seconds it takes for a swimmer to hear a single, hand-held, starting signal is given by the formula below, where (x,y) is the location of the starter (in meters), (0.p) is the location of the swimmer (in meters), and C is the air temperature (in degrees Celsius). Assume that the starter is located at the point (4,-2). Answer parts a and b below. √√x² + (y-p)² t(x,y.p.C)= 331.45+0.6C a. Calculate t(4, -2,30,20) and t(4, -2,20,20). Could the difference in time change the outcome of a race? t(4, -2,30,20) = (Round to five decimal places as needed.) Ay p Swimmer Starter (4,-2)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Text Transcription for Educational Website:**
The amount of time in seconds it takes for a swimmer to hear a single, hand-held, starting signal is given by the formula below, where (x, y) is the location of the starter (in meters), (0, p) is the location of the swimmer (in meters), and C is the air temperature (in degrees Celsius). Assume that the starter is located at the point (4, -2). Answer parts a and b below.
\[ t(x, y, p, C) = \frac{\sqrt{(x^2 + (y - p)^2)}}{331.45 + 0.6C} \]
**Diagram Explanation:**
In the diagram, a coordinate plane is shown:
- The x-axis is horizontal, and the y-axis is vertical.
- The starter's position is marked at (4, -2).
- A point labeled "Swimmer" is situated along the vertical line where x = 0.
**Problem Part:**
a. Calculate \( t(4, -2, 30, 20) \) and \( t(4, -2, 20, 20) \). Could the difference in time change the outcome of a race?
\[ t(4, -2, 30, 20) = [\_\_\_\_\_] \] (Round to five decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46a4dff8-7f9e-4127-9d1e-ef0349b76ae2%2Fe395a7bf-1f21-40d0-9e22-bbd7450966fb%2Fijchx8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Text Transcription for Educational Website:**
The amount of time in seconds it takes for a swimmer to hear a single, hand-held, starting signal is given by the formula below, where (x, y) is the location of the starter (in meters), (0, p) is the location of the swimmer (in meters), and C is the air temperature (in degrees Celsius). Assume that the starter is located at the point (4, -2). Answer parts a and b below.
\[ t(x, y, p, C) = \frac{\sqrt{(x^2 + (y - p)^2)}}{331.45 + 0.6C} \]
**Diagram Explanation:**
In the diagram, a coordinate plane is shown:
- The x-axis is horizontal, and the y-axis is vertical.
- The starter's position is marked at (4, -2).
- A point labeled "Swimmer" is situated along the vertical line where x = 0.
**Problem Part:**
a. Calculate \( t(4, -2, 30, 20) \) and \( t(4, -2, 20, 20) \). Could the difference in time change the outcome of a race?
\[ t(4, -2, 30, 20) = [\_\_\_\_\_] \] (Round to five decimal places as needed.)
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