You pull out the plug from the bathtub. After 40 seconds, there are 13 gallons of water left in the tub. One minute after you pu
ll the plug, there are 10 gallons left.
Assume that the number of gallons varies linearly with the time since the plug was pulled.
Write the particular equation expressing the number of gallons (g) left in the tub in terms of the number of seconds (s) since you pulled the plug.
Assume that the number of gallons varies linearly with the time since the plug was pulled.
Write the particular equation expressing the number of gallons (g) left in the tub in terms of the number of seconds (s) since you pulled the plug.
1 answer:
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The area of the figure is 40 units. (rounded off from 39.998 units)
Step-by-step explanation:
1. Area of the figure = Area of Rectangle + Area of Parallelogram.
2. Naming points:
Let the rectangle consist of points A(-6,-1), B(-5,-5), C(3,-3) and D(2,1).
Let the parallelogram consist of points C(3,-3), D(2,1), E(2,7) and F(3,3).
3. Each coordinate has a point on the x-axis and a point on the y-axis. We shall refer to these points as x', x'' ,x''' and so on corresponding to the x-axis values of A, B, C and so on in that order till F. For the y-axis points, we will name them in the series of y', y'', y''' and so on.
In simple words, in A(-6,1), x' = -6; y' = -1
4. Formula for finding area:
Area of a rectangle = length (l) × width (w)
Area of a parallelogram = base (b) x height (h)
5. Finding area of the rectangle:
l = AD =
, i.e. AD =
, i.e. AD = √68 = 8.246 (rounded to 3 decimals) = l
Now, w = AB =
, i.e. AB =
, i.e. AB = √17 = 4.123 (rounded to 3 decimals) = w
Area of rectangle = l x w = 8.246 x 4.123 = 33.998 units.
6. Finding area of the parallelogram:
b = DE = 6 units (we can observe this from the graph, i.e. points from 1 to 7 on the y axis)
h = Height is the line drawn perpendicular to the base from point F, which as we can see is 1 unit long.
Hence, Area of parallelogram = b x h = 6 x 1 = 6 units.
7. Now, adding both, we can arrive at the final answer.
Area of the figure = Area of rectangle + Area of parallelogram,
i.e. 33.998 units + 6 units = 39.998 units. (can be rounded off to 40 units)