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The function ​s(x)equals=startfraction 3600 over 60 plus x endfraction equals 3600 left parenthesis 60 plus x right parenthesis superscript negative 1 3600 60+x=3600(60+x)−1 gives a​ person's average speed in miles per hour if he or she travels one mile in x seconds more or less than 60 seconds. use a linear approximation to s at 0 to find a​ person's approximate average speed if he or she travels one mile in 5656 seconds. what is his or her exact​ speed?

Respuesta :

Solution:

[tex]S(x)=\frac{3600}{60+x}-1\\\\ S'(x)= 3600\times\frac{-1}{(60+x)^2}[/tex]

If , y = [tex]\frac{1}{x}, {\text{then y' means it's derivative}= \frac{-1}{x^2}[/tex]

As average speed = Rate of change of distance

for s=0 , 3600=60+x

x= 3540 seconds

for s= 1 mile, x= 5656 seconds

As , average speed =  [tex]\frac{S_{2}-S_{1}}{t_{2}-t_{1}}=\frac{1-0}{5656-3540}=\frac{1}{2116}[/tex]m/sec=0.0004725 m/sec

ankitprmr2

Speed can be calculated as the ratio of change in position of an object with respect to time. Thus, "his or her exact speed is  0.0004725 meters per second.

Given,

[tex]S(x)=\dfrac{3600}{60+x}-1[/tex]

Here, x is in second, and S(x) is the position of the object, thus the derivative of S(x) gives speed function.

Differentiate the above expression with respect to the x.

[tex]S'(x)=\dfrac{-1}{(60+x)^2} \times 3600[/tex]

Thus, the above function is the speed function.

To calculate average speed, we need to calculate the positions.

Therefore,

For s=0 x=3540 s

he or she travels one mile in 5656 seconds

Average speed is the rate of change of the positions.

[tex]\begin{aligned}Average\;speed&=\dfrac{S_2-S_1}{t_2-t_1}\\&=\dfrac{1-0}{5656-3540}\\&=\dfrac{1}{2116}\\&=0.0004725 \end{aligned}[/tex]

Thus, the average speed is 0.0004725 miles per second.

Learn more about the average speed, please refer to the link:

https://brainly.com/question/17277454