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Answer :
Let's solve the problem step-by-step.
We're given that the temperature [tex]\( T \)[/tex] of the water in the ocean is inversely proportional to the depth [tex]\( x \)[/tex] in meters. The relationship is given by the formula:
[tex]\[ T = \frac{4500}{x} \][/tex]
We need to find the difference in temperature of the water at two different depths: 1200 meters and 3750 meters.
### Step 1: Calculate the temperature at a depth of 1200 meters.
Using the formula, substitute [tex]\( x = 1200 \)[/tex]:
[tex]\[ T = \frac{4500}{1200} \][/tex]
This calculation gives a water temperature of 3.75°C at 1200 meters depth.
### Step 2: Calculate the temperature at a depth of 3750 meters.
Similarly, substitute [tex]\( x = 3750 \)[/tex] into the formula:
[tex]\[ T = \frac{4500}{3750} \][/tex]
This calculation gives a water temperature of 1.2°C at 3750 meters depth.
### Step 3: Find the difference in temperature between the two depths.
To find the difference in temperature, subtract the temperature at 3750 meters from the temperature at 1200 meters:
[tex]\[ \text{Difference} = 3.75 - 1.2 \][/tex]
This results in a difference of 2.55°C.
Therefore, the difference in temperature between the water at a depth of 1200 meters and at a depth of 3750 meters is 2.55°C.
We're given that the temperature [tex]\( T \)[/tex] of the water in the ocean is inversely proportional to the depth [tex]\( x \)[/tex] in meters. The relationship is given by the formula:
[tex]\[ T = \frac{4500}{x} \][/tex]
We need to find the difference in temperature of the water at two different depths: 1200 meters and 3750 meters.
### Step 1: Calculate the temperature at a depth of 1200 meters.
Using the formula, substitute [tex]\( x = 1200 \)[/tex]:
[tex]\[ T = \frac{4500}{1200} \][/tex]
This calculation gives a water temperature of 3.75°C at 1200 meters depth.
### Step 2: Calculate the temperature at a depth of 3750 meters.
Similarly, substitute [tex]\( x = 3750 \)[/tex] into the formula:
[tex]\[ T = \frac{4500}{3750} \][/tex]
This calculation gives a water temperature of 1.2°C at 3750 meters depth.
### Step 3: Find the difference in temperature between the two depths.
To find the difference in temperature, subtract the temperature at 3750 meters from the temperature at 1200 meters:
[tex]\[ \text{Difference} = 3.75 - 1.2 \][/tex]
This results in a difference of 2.55°C.
Therefore, the difference in temperature between the water at a depth of 1200 meters and at a depth of 3750 meters is 2.55°C.
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