The area under the graph line
1 answer:
<u>The statement is true</u>: the area under the graph line made with the x-axis
represents the change in position of the object on a velocity versus time
graph.
Reasons:
The area under the velocity time graph is given by the integration of the function for the velocity over the time interval.
A constant velocity is an horizontal line and the integration of a constant with time, gives the product of time and the constant, which is area under the rectangular graph.
Therefore, the area under the graph line made with the x-axis represents the change in position of the object on a velocity versus time graph.
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The statement that does not match the others is the one at lower right.
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The barn's volume can be decomposed into a rectangular prism and a triangular one. Thus the <em>upper right</em> expression is a true represenation of the barn's volume:
... Volume of triangular prism + Volume of rectangular prism
The volume of a <em>rectangular prism</em> is the product of its dimensions. The dimensions of the rectangular prism portion of the barn's volume are a, b, c, so the volume of that portion is ...
... Volume of rectangular prism = a·b·c
The volume of a <em>triangular prism</em> is the area of the triangular base multiplied by the length of the prism. Here, the triangular base has base dimension b and height (d-c), so its area is ...
... Area of triangular barn end = (1/2)b(d-c)
Since the length of the barn is "a", the volume of the triangular prism is ...
... Volume of triangular prism = (1/2)b(d-c)a = (1/2)·a·b·(d-c)
The <em>total volume</em> is the sum of the volumes of the parts ...
... a·b·c + (1/2)·a·b·(d-c) . . . . . . matches the <em>upper right</em> selection
This can be factored by removing a·b to outside parentheses:
... a·b·((1/2)·(d-c) + c) . . . . . . . . . matches the <em>lower left</em> selection
___
Since the two left selections match the one at upper right, the odd one is the one at lower left.
