Answer:
the answer is
Step-by-step explanation:
Answer:
9x+ (-1/8)
Step-by-step explanation:
add the fractions
Answer:
![y = \frac{9x^2}{2} + c](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B9x%5E2%7D%7B2%7D%20%2B%20c)
Step-by-step explanation:
Given
![\int\limits^ _](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%20_)
![(x + 8x) dx](https://tex.z-dn.net/?f=%28x%20%2B%208x%29%20dx)
Required
(a) Integrate
(b) Check using differentiation
To integrate, we make use of the following formula;
if
![\frac{dy}{dx} = \int\limits^{} _{} ax^n](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cint%5Climits%5E%7B%7D%20_%7B%7D%20ax%5En)
then
![y = \frac{ax^{n+1}}{n+1}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Bax%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D)
So; ![\int\limits^ _](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%20_)
becomes
![y = \frac{x^{1+1}}{1+1} + \frac{8x^{1+1}}{1+1} + c](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Bx%5E%7B1%2B1%7D%7D%7B1%2B1%7D%20%2B%20%5Cfrac%7B8x%5E%7B1%2B1%7D%7D%7B1%2B1%7D%20%2B%20c)
![y = \frac{x^{2}}{2} + \frac{8x^{2}}{2} + c](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%20%2B%20%5Cfrac%7B8x%5E%7B2%7D%7D%7B2%7D%20%2B%20c)
![y = \frac{x^{2}}{2} + 4x^2 + c](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%20%2B%204x%5E2%20%2B%20c)
Take LCM
![y = \frac{x^{2} + 8x^2}{2} + c](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7Bx%5E%7B2%7D%20%2B%208x%5E2%7D%7B2%7D%20%2B%20c)
![y = \frac{9x^2}{2} + c](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B9x%5E2%7D%7B2%7D%20%2B%20c)
To check using differentiation, we make use of
if
, then
![\frac{dy}{dx} = nax^{n-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20nax%5E%7Bn-1%7D)
Using this formula
becomes
![\frac{dy}{dx} = 2 * \frac{9x^{2-1}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20%2A%20%5Cfrac%7B9x%5E%7B2-1%7D%7D%7B2%7D)
![\frac{dy}{dx} = 2 * \frac{9x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20%2A%20%5Cfrac%7B9x%7D%7B2%7D)
![\frac{dy}{dx} =9x](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D9x)
![9x = x + 8x](https://tex.z-dn.net/?f=9x%20%3D%20x%20%20%2B%208x)
So;
![\frac{dy}{dx} = x + 8x](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20x%20%2B%208x)
He used 74.4 lbs of type A coffee.
If he is using a mixture of two divide the total of cost by 2 to get the amount of what one of the coffee costed, then divide that by 5.55 and you get the answer.
1.64
2. 95%
Hope this helps you.