Mathematics, 21.07.2019 01:30 quissowavyquis8484

Suppose the initial position of an object is zero, and the object moves with constant acceleration. which part of a velocity vs. time graph can be used to calculate the displacement of the object? the area of the rectangle under the line the area of the rectangle above the line the area of the rectangle plus the area of the triangle under the line the area of the rectangle plus the area of the triangle above the line

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If acceleration is constant (and apparently positive), then velocity increases linearly, so the graph of velocity with respect to time is a line with positive slope. The region between this line and the horizontal axis would then be a triangle or a trapezoid, depending on the object's velocity at the start (which we don't necessarily know). To get the object's displacement, one would have to integrate the velocity, which in terms of the graph corresponds to the area of this triangle/trapezoid.

But the given options are quite vague... We can rule out the first two, since they seem to use "line" to refer to a constant function with 0 slope, which we know is not the case with the velocity graph in this situation.

The other two options are ambiguous as well, but it seems like the third is the right one.

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

Me if you can and if you finished this lesson on edg- comment you.

Answer from: Quest

option a is correct.

$\frac{\text{original height}}{\text{original base}}=\frac{\text{reduction height}}{\text{reduction base}}$

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

$\frac{\text{original height}}{\text{original base}}=\frac{\text{reduction height}}{\text{reduction base}}$

Which is the scale factor proportion for the reduction shown? answers are on picture.

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Suppose the initial position of an object is zero, and the object moves with constant acceleration....

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