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guajiro [1.7K]
3 years ago
9

A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t)=(t)ln(5t). Find the acceleration of the par

ticle when the velocity is first zero
5e
5e^2
e
None of these
Mathematics
1 answer:
lyudmila [28]3 years ago
5 0

Answer:

a(\frac{1}{5e})=5e

Step-by-step explanation:

we are given equation for position function as

s(t)=tln(5t)

Since, we have to find acceleration

For finding acceleration , we will find second derivative

s'(t)=\frac{d}{dt}\left(t\ln \left(5t\right)\right)

=\frac{d}{dt}\left(t\right)\ln \left(5t\right)+\frac{d}{dt}\left(\ln \left(5t\right)\right)t

=1\cdot \ln \left(5t\right)+\frac{1}{t}t

s'(t)=\ln \left(5t\right)+1

now, we can find derivative again

s''(t)=\frac{d}{dt}\left(\ln \left(5t\right)+1\right)

=\frac{d}{dt}\left(\ln \left(5t\right)\right)+\frac{d}{dt}\left(1\right)

=\frac{1}{t}+0

a(t)=\frac{1}{t}

Firstly, we will set velocity =0

and then we can solve for t

v(t)=s'(t)=\ln \left(5t\right)+1=0

we get

t=\frac{1}{5e}

now, we can plug that into acceleration

and we get

a(\frac{1}{5e})=\frac{1}{\frac{1}{5e}}

a(\frac{1}{5e})=5e


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Write an equation for each linear function described. Show your work. The graph of the function passes through the point (2,1),
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Step-by-step explanation:

As

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so

x             y

2             1

3             5

4             9

5             13

6             17

and so on

From the table:

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(2,\:1\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)

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As the slope-intercept form of the line is

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putting m=4 and any point, let say (2, 1) to find y-intercept 'b'.

1=\left(4\right)2+b

8+b=1

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So putting b=-7 and m=4  in the slope-intercept form of the line

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Answer:

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Step-by-step explanation:

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∑ r^k = (1 - r^N)/(1 - r)

if we have the summation between k = 0 and k = ∞ - 1 = ∞

(here we used that ∞ is really big, then ∞ - 1 = ∞)

In the numerator we will have the term r^∞, if 0 < r < 1, then r^∞ = 0.

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In our case, we can rewrite our summation as:

3*∑ (1/2)^n

for n = 0 to  n = ∞

You can see that i changed the limits for n, this does not really matter because we are summing between a number and infinity, the only thing you need to take care is that now the power is n, instead of (n - 1)

Then we have r = (1/2) which is clearly smaller than 1.

then (1/2)

Then this summation is equal to:

3*∑ (1/2)^n = 3*( 1/(1 - 1/2)) = 3*( 1/( 2/2 - 1/2)) = 3*( 1/(1/2)) = 3*2 = 6

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The best answer from the options that proves that the residual plot shows that the line of best fit is appropriate for the data is: ( Statement 1 ) Yes, because the points have no clear pattern

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1            3.5           4.06             -0.56

2           2.3           2.09             0.21

3            1.1            0.12               0.98

4           2.2           -1.85              4.05

5          -4.1            -3.82            -0.28

The residual value is calculated as follows using this formula: ( Given - predicted )

1) ( 3.5 - 4.06 ) = -0.56

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5) ( -4.1 - (-3.82) = -0.28

Residual values are the difference between the given values and the predicted values in a given data set and the residual plot is used to represent these values .

attached below is the residual plot of the data set

hence we can conclude from the residual plot attached below that the line of best fit is appropriate for the data because the points have no clear pattern ( i.e. scattered )

learn more about residual plots : brainly.com/question/16821224

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