-1.5 is the answer because it is 75
Answer:
See Below.
Step-by-step explanation:
We want to show that the function:
![f(x) = e^x - e^{-x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20e%5Ex%20-%20e%5E%7B-x%7D)
Increases for all values of <em>x</em>.
A function is increasing whenever its derivative is positive.
So, find the derivative of our function:
![\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5Be%5Ex%20-%20e%5E%7B-x%7D%5Cright%5D)
Differentiate:
![\displaystyle f'(x) = e^x - (-e^{-x})](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20e%5Ex%20-%20%28-e%5E%7B-x%7D%29)
Simplify:
![f'(x) = e^x+e^{-x}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20e%5Ex%2Be%5E%7B-x%7D)
Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of <em>x.</em>
Answer:
A ) The money which Andre pay for the bike is $ 67.30
B ) The money which Andre pay for the bike is $ 76.92
Step-by-step explanation:
Given as :
The wholesale cost or market price of the bike = m.p = $ 96.15
A ) The discount percentage = 30 %
Let The selling price of the bike after discount = s.p
Now ,
Discount % = ![\dfrac{m.p - s. p }{m . p}](https://tex.z-dn.net/?f=%5Cdfrac%7Bm.p%20-%20s.%20p%20%7D%7Bm%20.%20p%7D)
or, 30 % = 1 - ![\dfrac{s. p }{m . p}](https://tex.z-dn.net/?f=%5Cdfrac%7Bs.%20p%20%7D%7Bm%20.%20p%7D)
or,
= 1 - ![\dfrac{s. p }{96.15}](https://tex.z-dn.net/?f=%5Cdfrac%7Bs.%20p%20%7D%7B96.15%7D)
Or,
= 1 - ![\dfrac{30 }{100}](https://tex.z-dn.net/?f=%5Cdfrac%7B30%20%7D%7B100%7D)
or,
= ![\dfrac{100 - 30 }{100}](https://tex.z-dn.net/?f=%5Cdfrac%7B100%20-%2030%20%7D%7B100%7D)
Or,
= ![\dfrac{70}{100}](https://tex.z-dn.net/?f=%5Cdfrac%7B70%7D%7B100%7D)
Or, s. p =
× 96.15
∴ s.p = $ 67.305
So, He will pay $ 67.30
Hence The money which Andre pay for the bike is $ 67.30 . Answer
B ) If the bike is discounted by 20 % , let The selling price = s.p'
So,
Discount % = ![\dfrac{m.p - s. p }{m . p}](https://tex.z-dn.net/?f=%5Cdfrac%7Bm.p%20-%20s.%20p%20%7D%7Bm%20.%20p%7D)
or, 20 % = 1 - ![\dfrac{s. p' }{m . p}](https://tex.z-dn.net/?f=%5Cdfrac%7Bs.%20p%27%20%7D%7Bm%20.%20p%7D)
or,
= 1 - ![\dfrac{s. p' }{96.15}](https://tex.z-dn.net/?f=%5Cdfrac%7Bs.%20p%27%20%7D%7B96.15%7D)
Or,
= 1 - ![\dfrac{20 }{100}](https://tex.z-dn.net/?f=%5Cdfrac%7B20%20%7D%7B100%7D)
or,
= ![\dfrac{100 - 20 }{100}](https://tex.z-dn.net/?f=%5Cdfrac%7B100%20-%2020%20%7D%7B100%7D)
Or,
= ![\dfrac{80}{100}](https://tex.z-dn.net/?f=%5Cdfrac%7B80%7D%7B100%7D)
Or, s. p' =
× 96.15
∴ s.p' = $ 76.92
So, He will pay $ 76.92
Hence The money which Andre pay for the bike is $ 76.92 . Answer
I think you are asking for the quotient of the numbers because base from the choices the units are meters per second and the given has units of meters and seconds. So, the quotient of the numbers is 43.218 meters per second which is option B.
The pong will be at 3.5 m