Question

To find a formula for the function A(m), which is the pressure that a pest experiences at a depth of d feet, we first have R(m)=0.2m+2m, which represents the relationship between the depth m and the pressure. Now, we want to express A(m) in terms of P(π(m)).

Given R(m)=0.2m+2m, let's express it as P(m) since R(m) represents pressure:
P(m)=0.2m+2m

Answer 1

To define the pressure function A(m), we use the relationship m = pAh for depth and pressure and we express pressure as P(m) = 0.2m + 2m. We need to substitute the value of m as obtained from the function π(m) into the pressure formula to get A(m). Pressure is known to increase linearly with depth in a fluid of constant density.

Step-by-step explanation:

To find a formula for the pressure function A(m), we first acknowledge that we have been given the relationship represented by R(m) for pressure depending on the depth m. Since R(m) = 0.2m + 2m, we will redefine this as P(m) which is the pressure due to water depth. We know that pressure in a fluid with a constant density increases linearly with depth, and we are given the relationship m = pAh, where p is the density, A is the cross-sectional area, and h is the depth.

When we substitute m = pAh into the original equation for pressure, we're trying to express the pressure A(m) in terms of P applied to the function of depth π(m). The formula for average pressure due to the weight of a fluid is P = hρg, where h is the depth, ρ is the density of the fluid, and g is the acceleration due to gravity. To find the depth at which the pressure equals a certain value, we solve the equation for h, getting h = P / (ρg).

Ultimately, if we have a specific function π(m) that relates to pressure in some way, we would insert the expression for m from π(m) into the P(m) formula to get the function A(m).