Question

Find the area of a parallelogram bounded by the y-axis, the line x = 3, the line f(x) = 12x, and the line parallel to f(x) passing through (2, 7).

Answer 1

To find the area of the parallelogram, determine the height and base, then apply the formula for the area of a parallelogram.

Step-by-step explanation:

To find the area of the parallelogram bounded by the y-axis, the line x = 3, the line f(x) = 12x, and the line parallel to f(x) passing through (2, 7), we can follow these steps:

1. Determine the height of the parallelogram, which is the distance between the line f(x) = 12x and the line parallel to it passing through (2, 7). This can be calculated by substituting x = 2 into the equation f(x) = 12x and solving for y.
2. Calculate the base of the parallelogram, which is the difference between the x-values at which the parallelogram is bounded.
3. Use the formula for the area of a parallelogram, A = base * height, to find the area of the parallelogram.

Applying these steps, the area of the parallelogram can be found.