Answer:
The maximum possible error of in measurement of the angle is ![d\theta_1 =(14.36p)^o](https://tex.z-dn.net/?f=d%5Ctheta_1%20%20%3D%2814.36p%29%5Eo)
Step-by-step explanation:
From the question we are told that
The angle of elevation is ![\theta_1 = 15 ^o = \frac{\pi}{12}](https://tex.z-dn.net/?f=%5Ctheta_1%20%20%3D%20%2015%20%5Eo%20%3D%20%20%5Cfrac%7B%5Cpi%7D%7B12%7D)
The height of the tree is h
The distance from the base is D
h is mathematically represented as
Note : this evaluated using SOHCAHTOA i,e
![tan\theta = \frac{h}{D}](https://tex.z-dn.net/?f=tan%5Ctheta%20%20%3D%20%20%5Cfrac%7Bh%7D%7BD%7D)
Generally for small angles the series approximation of ![tan \theta \ is](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%5C%20%20is)
![tan \theta = \theta + \frac{\theta ^3 }{3}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%20%3D%20%20%5Ctheta%20%20%2B%20%5Cfrac%7B%5Ctheta%20%5E3%20%7D%7B3%7D)
So given that ![\theta = 15 \ which \ is \ small](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%2015%20%5C%20which%20%5C%20is%20%5C%20small)
![h = D (\theta + \frac{\theta^3}{3} )](https://tex.z-dn.net/?f=h%20%3D%20D%20%28%5Ctheta%20%2B%20%5Cfrac%7B%5Ctheta%5E3%7D%7B3%7D%20%29)
![dh = D (1 + \theta^2) d\theta](https://tex.z-dn.net/?f=dh%20%3D%20D%20%281%20%2B%20%5Ctheta%5E2%29%20d%5Ctheta)
=> ![\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bh%7D%20%3D%20%20%5Cfrac%7B1%20%2B%20%5Ctheta%20%5E2%7D%7B%5Ctheta%20%2B%20%5Cfrac%7B%5Ctheta%5E3%7D%7B3%7D%20%7D%20d%20%5Ctheta)
Now from the question the relative error of height should be at most
%
=> ![\frac{dh}{h} = \pm p](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bh%7D%20%3D%20%20%20%5Cpm%20p)
=> ![\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p](https://tex.z-dn.net/?f=%5Cfrac%7B1%20%2B%20%5Ctheta%20%5E2%7D%7B%5Ctheta%20%2B%20%5Cfrac%7B%5Ctheta%5E3%7D%7B3%7D%20%7D%20d%20%5Ctheta%20%20%3D%20%5Cpm%20p)
=> ![d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p](https://tex.z-dn.net/?f=d%5Ctheta%20%20%3D%20%20%5Cpm%20%20%5Cfrac%7B%5Ctheta%20%2B%20%20%5Cfrac%7B%5Ctheta%5E3%7D%7B3%7D%20%7D%7B1%2B%20%5Ctheta%20%5E2%7D%20%2A%20%20%20%20%5C%20p)
So for ![\theta_1](https://tex.z-dn.net/?f=%5Ctheta_1)
![d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p](https://tex.z-dn.net/?f=d%5Ctheta_1%20%20%3D%20%20%5Cpm%20%20%5Cfrac%7B%5Ctheta_1%20%2B%20%20%5Cfrac%7B%5Ctheta%5E3_1%20%7D%7B3%7D%20%7D%7B1%2B%20%5Ctheta_1%20%5E2%7D%20%2A%20%20%20%20%5C%20p)
substituting values
![d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p](https://tex.z-dn.net/?f=d%20%5B%5Cfrac%7B%5Cpi%7D%7B12%7D%20%5D%20%20%3D%20%20%5Cpm%20%20%5Cfrac%7B%5B%5Cfrac%7B%5Cpi%7D%7B12%7D%20%5D%20%2B%20%20%5Cfrac%7B%5B%5Cfrac%7B%5Cpi%7D%7B12%7D%20%5D%5E3%20%7D%7B3%7D%20%7D%7B1%2B%20%5B%5Cfrac%7B%5Cpi%7D%7B12%7D%20%5D%20%5E2%7D%20%2A%20%20%20%20%5C%20p)
=> ![d\theta_1 = 0.25 p](https://tex.z-dn.net/?f=d%5Ctheta_1%20%20%3D%200.25%20p)
Converting to degree
![d\theta_1 = (0.25* 57.29) p](https://tex.z-dn.net/?f=d%5Ctheta_1%20%20%3D%20%280.25%2A%2057.29%29%20p)
![d\theta_1 =(14.36p)^o](https://tex.z-dn.net/?f=d%5Ctheta_1%20%20%3D%2814.36p%29%5Eo)
Answer:
papá fríoStep-by-step explanation:
Property/homeowners insurance. Apex confirmed
You would divide the cheetahs distance which is 300 feet by the cheetahs time which is 2.92 seconds
distance÷time
300÷2.92= 102.7 seconds or 103 seconds if you round up
the cheetahs speed is 102.7 seconds or 103 seconds
Answer:
c
Step-by-step explanation: