We are given
![f(x)=e^{x} cosh(x)](https://tex.z-dn.net/?f=f%28x%29%3De%5E%7Bx%7D%20cosh%28x%29)
Since,
and
are multiplied
so, we will use product rule of derivative
![\mathrm{Apply\:the\:Product\:Rule}:\quad \left(f\cdot g\right)'=f\:'\cdot g+f\cdot g'](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3AProduct%5C%3ARule%7D%3A%5Cquad%20%5Cleft%28f%5Ccdot%20g%5Cright%29%27%3Df%5C%3A%27%5Ccdot%20g%2Bf%5Ccdot%20g%27)
![f'(x)=\frac{d}{dx}\left(e^x\right)\cosh \left(x\right)+\frac{d}{dx}\left(\cosh \left(x\right)\right)e^x](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28e%5Ex%5Cright%29%5Ccosh%20%5Cleft%28x%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Ccosh%20%5Cleft%28x%5Cright%29%5Cright%29e%5Ex)
we know that
![\frac{d}{dx}\left(e^x\right)=e^x](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28e%5Ex%5Cright%29%3De%5Ex)
and
![\frac{d}{dx}\left(\cosh \left(x\right)\right)=\sinh \left(x\right)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Ccosh%20%5Cleft%28x%5Cright%29%5Cright%29%3D%5Csinh%20%5Cleft%28x%5Cright%29)
so, we can plug these values
and we get
...............Answer
Ratio compares two things. The length of the trail, in reality, is 6.75 km.
<h3>What is the scale ratio?</h3>
A scaling ratio helps us to compare two things.
Given to us
The scale on the map states that 2 centimeters represent 3 kilometers.
Length of the trail on the map, L = 4.5 cm = 0.045 m
As we know that 2 centimeters represent 3 kilometers. therefore,
![\rm \dfrac{Map}{Real} = \dfrac{0.02\ m}{3000\ m}](https://tex.z-dn.net/?f=%5Crm%20%5Cdfrac%7BMap%7D%7BReal%7D%20%3D%20%5Cdfrac%7B0.02%5C%20m%7D%7B3000%5C%20m%7D)
We know that the Length of the trail on the map is 0.045 m,
![\rm \dfrac{L}{L'} = \dfrac{0.02\ m}{3000\ m}](https://tex.z-dn.net/?f=%5Crm%20%5Cdfrac%7BL%7D%7BL%27%7D%20%3D%20%5Cdfrac%7B0.02%5C%20m%7D%7B3000%5C%20m%7D)
Substitute the value,
![\rm \dfrac{0.045}{L'} = \dfrac{0.02\ m}{3000\ m}\\\\L' = 6750\ m\\\\L' = 6.750\ km](https://tex.z-dn.net/?f=%5Crm%20%5Cdfrac%7B0.045%7D%7BL%27%7D%20%3D%20%5Cdfrac%7B0.02%5C%20m%7D%7B3000%5C%20m%7D%5C%5C%5C%5CL%27%20%3D%206750%5C%20m%5C%5C%5C%5CL%27%20%3D%206.750%5C%20km)
Hence, the length of the trail, in reality, is 6.75 km.
Learn more about Ratio:
brainly.com/question/1504221
Answer:
x= -1.7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Aubrey would be able to run 9 miles in ninety minutes.
90 minutes=1.5 hours
6*1.5=9
Hope this helps
In Euclidean geometry, the sum of the measures of the interior anlges of a pentagon is 540°.
The sum of the measures of the interior angles of a pentagon would be different in spherical geometry because A.) THE SUM WOULD BE GREATER THAN 540°