Find the area of a parallelogram bounded by the y-axis, the line x=3, the line f(x)=1+2x, and the line parallel to f(x) passing through (2, 7).

  6 square units

Step-by-step explanation:

The parallel line has equation ...

  y -7 = 2(x -2)

  y = 2x + 3

The y-intercept of this one differs from the given line by 3-1 = 2, so that is the length of the "base" of the parallelogram. The "height" is the distance between the parallel lines x=0 and x=3, which is 3-0 = 3. Then the area is ...

  A = bh = 2·3 = 6 . . . . square units

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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