what or how would i solve the following i don't need the answer i want to do it but how would i solve this.
Water pressure (p) in the ocean is 2.3 tons per square inch at a depth (d) of 2miles and 3.45 tons per square inch at depth of 3 miles.
How do i find the linear equation using (d,p) for htese data points?
How do i find the pressure at a depth of 4miles?
Make an equation:
Pressure= m*depth + k
Put in the two values, you will have two equations. Solve for m, and k.
To find the linear equation using the data points (d, p), where d represents the depth and p represents the water pressure, you can follow these steps:
1. Assign one data point to each variable. Let's use (d1, p1) = (2 miles, 2.3 tons per square inch) and (d2, p2) = (3 miles, 3.45 tons per square inch).
2. Write the linear equation in the form: Pressure = m * depth + k.
3. Substitute the values from the first data point into the equation:
p1 = m * d1 + k,
2.3 = m * 2 + k.
4. Substitute the values from the second data point into the equation:
p2 = m * d2 + k,
3.45 = m * 3 + k.
5. Now, you have two equations with two variables (m and k). You can solve these equations simultaneously to find the values of m and k.
Equations:
2.3 = 2m + k (Equation 1)
3.45 = 3m + k (Equation 2)
6. Subtract Equation 1 from Equation 2 to eliminate k:
3.45 - 2.3 = 3m + k - (2m + k),
1.15 = m.
7. Substitute the value of m back into Equation 1 or Equation 2 to find k:
2.3 = 2(1.15) + k,
2.3 = 2.3 + k,
k = 0.
8. Therefore, the linear equation relating depth (d) and water pressure (p) is:
Pressure = 1.15 * depth.
To find the pressure at a depth of 4 miles, substitute the value of depth (d = 4 miles) into the equation:
Pressure at 4 miles = 1.15 * 4.