Answer :
To find the difference in temperature of the water at different depths, we follow the relationship given in the problem: the temperature [tex]\( T \)[/tex] is inversely proportional to the depth [tex]\( x \)[/tex]. This is represented by the formula:
[tex]\[ T = \frac{4500}{x} \][/tex]
Let's calculate the temperature at each specified depth and find their difference.
1. Calculate the temperature at a depth of 1200 meters:
Using the formula [tex]\( T = \frac{4500}{x} \)[/tex], substitute [tex]\( x = 1200 \)[/tex].
[tex]\[
T = \frac{4500}{1200} = 3.75^\circ C
\][/tex]
2. Calculate the temperature at a depth of 3750 meters:
Again using the formula, substitute [tex]\( x = 3750 \)[/tex].
[tex]\[
T = \frac{4500}{3750} = 1.2^\circ C
\][/tex]
3. Find the difference in temperature between the two depths:
Subtract the temperature at 3750 meters from the temperature at 1200 meters.
[tex]\[
\text{Difference} = 3.75 - 1.2 = 2.55^\circ C
\][/tex]
Therefore, the difference in the temperature of the water at a depth of 1200 meters and a depth of 3750 meters is [tex]\( 2.55^\circ C \)[/tex].
[tex]\[ T = \frac{4500}{x} \][/tex]
Let's calculate the temperature at each specified depth and find their difference.
1. Calculate the temperature at a depth of 1200 meters:
Using the formula [tex]\( T = \frac{4500}{x} \)[/tex], substitute [tex]\( x = 1200 \)[/tex].
[tex]\[
T = \frac{4500}{1200} = 3.75^\circ C
\][/tex]
2. Calculate the temperature at a depth of 3750 meters:
Again using the formula, substitute [tex]\( x = 3750 \)[/tex].
[tex]\[
T = \frac{4500}{3750} = 1.2^\circ C
\][/tex]
3. Find the difference in temperature between the two depths:
Subtract the temperature at 3750 meters from the temperature at 1200 meters.
[tex]\[
\text{Difference} = 3.75 - 1.2 = 2.55^\circ C
\][/tex]
Therefore, the difference in the temperature of the water at a depth of 1200 meters and a depth of 3750 meters is [tex]\( 2.55^\circ C \)[/tex].
