every rational number can be written as a fraction
Answer:
$978
Step-by-step explanation:
Given:
- y = amount of profit
- x = selling price of each widget
![y=-x^2+78x-543](https://tex.z-dn.net/?f=y%3D-x%5E2%2B78x-543)
To find the maximum amount of profit, differentiate the equation, set it to zero and solve for x. Substitute found value of x into the original equation.
<u>Differentiate equation</u>
![y=-x^2+78x-543](https://tex.z-dn.net/?f=y%3D-x%5E2%2B78x-543)
![\implies \dfrac{dy}{dx}=-2x+78](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bdy%7D%7Bdx%7D%3D-2x%2B78)
<u>Set differentiated equation to zero and solve for x</u>:
![\dfrac{dy}{dx}=0](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D0)
![\implies -2x+78=0](https://tex.z-dn.net/?f=%5Cimplies%20-2x%2B78%3D0)
![\implies 2x=78](https://tex.z-dn.net/?f=%5Cimplies%202x%3D78)
![\implies x=39](https://tex.z-dn.net/?f=%5Cimplies%20x%3D39)
<u>Maximum profit</u>
Substitute x = 39 into the equation:
![\implies -(39)^2+78(39)-543=978](https://tex.z-dn.net/?f=%5Cimplies%20-%2839%29%5E2%2B78%2839%29-543%3D978)
Therefore, max profit is $978
Answer:
-6/-5
-4/2
Step-by-step explanation:
I hope is correct
Answer:
$ 9.5 per person
Step-by-step explanation:
If it is $ 95 for 10 people then to find the unit rate per person is to just divide the total amount by the total number of people.
i.e, 95 / 10 = $ 9.5
Hope this helps you.
Answer:
30 <em>pages per hour</em>
Step-by-step explanation:
6 <em>pages per </em>1/5 <em>hour </em>
6 <em>x 5 = 30</em>
<em>1/5= </em><em>one whole would be five parts</em>
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