Let T(d) be the temperature of the seawater in the Mariana Trench d meters below the surface. Find a formula for p(x), the temperature x mm below the surface

Insert 1 for coefficients that do not change and 0 for shifts that are not necessary

My answers

p(x) = 1, T( ) x - 0 ) + 0

I'm trying to find what T is. I tried 1000 and then 100 but it appeared to be wrong. Or do I put 1 or 0 for T depending on shifts that are not necessary

To find a formula for p(x), the temperature x mm below the surface, we first need to determine the relationship between the temperature T(d) at a certain depth d meters below the surface and the temperature p(x) at x mm below the surface.

Given that T(d) represents the temperature of the seawater in the Mariana Trench at a depth d meters below the surface, we can assume that the temperature changes linearly with respect to depth. This means that for every meter we descend, there is a certain change in temperature, represented by the coefficient in the linear equation.

Now, let's break down the problem into smaller steps:

Step 1: Conversion between meters and millimeters
Since we are given the temperature in meters (d meters) and are asked to find the temperature in millimeters (x mm), we need to convert the units. Remember that 1 meter is equal to 1000 millimeters. So, d meters is equivalent to 1000d millimeters.

Step 2: Relationship equation
Considering the linear relationship between the depth (d) and temperature (T), we can write the equation as:
T(d) = m * d + b,
where m represents the coefficient of change in temperature per meter, and b represents the initial temperature at the surface (depth = 0 meters).

Step 3: Expressing in terms of millimeters
To express the equation in terms of x mm below the surface, we need to substitute d with the equivalent value in millimeters:
T(1000d) = m * (1000d) + b,
which simplifies to:
T(1000d) = 1000m * d + b.

Step 4: Equation for p(x)
Now we have an equation in terms of 1000d, but we want to find p(x) at x mm below the surface. Since 1000d represents the depth in millimeters, we can equate it to x:
1000d = x.

Simplifying for d:
d = x/1000.

Substituting d in the equation T(1000d):
T(1000(x/1000)) = 1000m * (x/1000) + b,
which simplifies to:
T(x) = mx + b.

Therefore, the formula for p(x), the temperature x mm below the surface, is:
p(x) = T(x) = mx + b.

To find the specific values of m and b, you would need additional information or data points.