Answer:
Number of cookies produced in 8 hour are 10,600 cookies.
Step-by-step explanation:
If the production rate of cookies in a bakery is 1325 cookies per hour, we need to tell how many cookies will be produced in 8 hour shift.
Number of cookies produced in 1 hour = 1325 cookies
Number of cookies produced in 8 hour = 1325 * 8
= 10,600 cookies.
So, Number of cookies produced in 8 hour are 10,600 cookies.
Step-by-step explanation:
90:120
9:12
3:4
Topic: ratio n proportions
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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)
Answer:
It would take 25 minutes for Patrick to complete the project alone.
Step-by-step explanation:
They did the project in 20 minutes, that is, 100% of the project, so:
![x + y = 1](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%201)
In which x is the percentage that Patrick worked and y is the percentage that Stewart worked.
Patrick works four times as quickly as Stewart, so x = 4y.
So
![x + y = 1](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%201)
![4y + y = 1](https://tex.z-dn.net/?f=4y%20%2B%20y%20%3D%201)
![5y = 1](https://tex.z-dn.net/?f=5y%20%3D%201)
![y = 0.2](https://tex.z-dn.net/?f=y%20%3D%200.2)
-----------
![x = 4y = 4*0.2 = 0.8](https://tex.z-dn.net/?f=x%20%3D%204y%20%3D%204%2A0.2%20%3D%200.8)
Patrick did 80% of the project in 20 minutes. We can solve this problem by a simple rule of three, in which the time it would take for him to complete the project alone is 100%. So
20 minutes - 0.8
x minutes - 1
![0.8x = 20](https://tex.z-dn.net/?f=0.8x%20%3D%2020)
![x = 25](https://tex.z-dn.net/?f=x%20%3D%2025)
It would take 25 minutes for Patrick to complete the project alone.