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ira [324]
4 years ago
7

The figure shows a graph of velocity versus time for a moving object. Which description matches the graph?

Mathematics
2 answers:
lubasha [3.4K]4 years ago
8 0

It's a decreasing line, so we can say this object is going slow in a constant velocity.

love history [14]4 years ago
7 0
<h2>Answer:</h2>

The description which matches the graph is:

  •          The object is slowing down.
<h2>Step-by-step explanation:</h2>

We are given a graph which represents the velocity of a moving object with respect to time.

The graph is a line which is decreasing continuously with the increasing time.

This means that the object is slowing down with the increasing time.

Also, we know that:

If the graph is a line then the slope is always constant.

This means that the acceleration is constant.

( since the ratio of change in velocity to change in time is the acceleration of the object which is the slope of the graph)

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Evaluate the integral by making an appropriate change of variables.
VARVARA [1.3K]

By inspecting the integrand, the "obvious" choice for substitution would be

<em>u</em> = <em>y</em> + <em>x</em>

<em>v</em> = <em>y</em> - <em>x</em>

<em />

Solving for <em>x</em> and <em>y</em>, we would have

<em>x</em> = (<em>u</em> - <em>v</em>)/2

<em>y</em> = (<em>u</em> + <em>v</em>)/2

in which case the Jacobian and its determinant are

J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12

The trapezoid <em>R</em> has two of its edges on the lines <em>x</em> + <em>y</em> = 8 and <em>x</em> + <em>y</em> = 9, so right away, we have 8 ≤ <em>u</em> ≤ 9.

Then for <em>v</em>, we observe that when <em>x</em> = 0 (the lowest edge of <em>R</em>), <em>v</em> = <em>y</em> ; similarly, when <em>y</em> = 0 (the leftmost edge of <em>R</em>), <em>v</em> = -<em>x</em>. So

-<em>x</em> ≤ <em>v</em> ≤ <em>y</em>

-(<em>u</em> - <em>v</em>)/2 ≤ <em>v</em> ≤ (<em>u</em> + <em>v</em>)/2

-<em>u</em> + <em>v</em> ≤ 2<em>v</em> ≤ <em>u</em> + <em>v</em>

-<em>u</em> ≤ <em>v</em> ≤ <em>u</em>

<em />

So, the integral becomes

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=\displaystyle\frac52\int_8^9\frac u7(\sin7-\sin(-7))\,\mathrm du

=\displaystyle\frac57\sin7\int_8^9u\,\mathrm du

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4 0
3 years ago
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Katena32 [7]

Answer:

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notice that the difference between the adjacent terms is 4.

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= -9 + (n-1) × 4

= -9 + 4n -4

= 4n -13

6 0
3 years ago
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