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5. For the following questions, use the following contour map of the function p(S, T) which describes seawater density in kilograms per cubic meter as a function of salinity (S) in parts per thousand, and temperature (T) in degrees Celsius. Temperature T (°C) 25 20 15 10 5 0 31.5 32.0 1.0230- 1.0235 1.0240 1.0245 1.0250 1.0255 1.0260 1.0265: 1.0270 B 32.5 33.0 33.5 34.0 Salinity (ppt) 34.5

5. For the following questions, use the following contour map of the function p(S, T) which describes seawater density in kilograms per cubic meter as a function of salinity (S) in parts per thousand, and temperature (T) in degrees Celsius. Temperature T (°C) 25 20 15 10 5 0 31.5 32.0 1.0230- 1.0235 1.0240 1.0245 1.0250 1.0255 1.0260 1.0265: 1.0270 B 32.5 33.0 33.5 34.0 Salinity (ppt) 34.5

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Please just answer c-e. Please show all work!

### Contour Map Analysis of Seawater Density To address the following questions, we will use the contour map provided for the function \( \rho(S, T) \), which describes seawater density in kilograms per cubic meter. This density is given as a function of salinity (\( S \)) in parts per thousand, and temperature (\( T \)) in degrees Celsius. #### Contour Map Explanation The contour map plots temperature (\( T \)) on the vertical axis (ranging from 0°C to 25°C) and salinity (\( S \)) on the horizontal axis (ranging from 31.5 to 34.5 parts per thousand). Contour lines on the map represent constant seawater densities. These are labeled with values such as 1.0220, 1.0230, etc. The labeled points A, B, and C are specific locations on the map where rates of change will be calculated. #### Questions (a) **Calculate the average rate of change of \( \rho \) with respect to \( T \) from B to A.** (b) **Calculate the average rate of change of \( \rho \) with respect to \( S \) from B to C.** (c) **At a fixed level of salinity, is seawater density an increasing or decreasing function of temperature?** (d) **At a fixed temperature, is seawater density an increasing or decreasing function of salinity?** (e) **Which of the points, A or B, does water density appear to be more sensitive to a change in temperature? Explain how you know.** ### Answers: **(a) Calculation:** - **Point B:** - Temperature \( T_B \): 5°C - Density \( \rho_B \): Approximately 1.0260 kg/m³ - **Point A:** - Temperature \( T_A \): 15°C - Density \( \rho_A \): Approximately 1.0250 kg/m³ Average rate of change of \( \rho \) with respect to \( T \): \[ \frac{\Delta \rho}{\Delta T} = \frac{\rho_A - \rho_B}{T_A - T_B} = \frac{1.0250 - 1.0260}{15 - 5} = \frac{-0.0010}{10} = -0.0001 \
Transcribed Image Text:### Contour Map Analysis of Seawater Density To address the following questions, we will use the contour map provided for the function \( \rho(S, T) \), which describes seawater density in kilograms per cubic meter. This density is given as a function of salinity (\( S \)) in parts per thousand, and temperature (\( T \)) in degrees Celsius. #### Contour Map Explanation The contour map plots temperature (\( T \)) on the vertical axis (ranging from 0°C to 25°C) and salinity (\( S \)) on the horizontal axis (ranging from 31.5 to 34.5 parts per thousand). Contour lines on the map represent constant seawater densities. These are labeled with values such as 1.0220, 1.0230, etc. The labeled points A, B, and C are specific locations on the map where rates of change will be calculated. #### Questions (a) **Calculate the average rate of change of \( \rho \) with respect to \( T \) from B to A.** (b) **Calculate the average rate of change of \( \rho \) with respect to \( S \) from B to C.** (c) **At a fixed level of salinity, is seawater density an increasing or decreasing function of temperature?** (d) **At a fixed temperature, is seawater density an increasing or decreasing function of salinity?** (e) **Which of the points, A or B, does water density appear to be more sensitive to a change in temperature? Explain how you know.** ### Answers: **(a) Calculation:** - **Point B:** - Temperature \( T_B \): 5°C - Density \( \rho_B \): Approximately 1.0260 kg/m³ - **Point A:** - Temperature \( T_A \): 15°C - Density \( \rho_A \): Approximately 1.0250 kg/m³ Average rate of change of \( \rho \) with respect to \( T \): \[ \frac{\Delta \rho}{\Delta T} = \frac{\rho_A - \rho_B}{T_A - T_B} = \frac{1.0250 - 1.0260}{15 - 5} = \frac{-0.0010}{10} = -0.0001 \
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