It would be 42 ,because it is increasing by 3 on the third week=39 fourth week=42.
Answer:
A
Step-by-step explanation:0.25 is a quarter so 1/4 is also a quarter so you juts add the subcalculus and you get the sum
The answer is 3/17
Explanation:
12+12+3=27
44-27=17
therefore students studing art = 17
as students studing art & biology = 3
the answer is 3/17
hope this helps :)
Answer:
![A = \int\limits^3__-3}{9}-{x^{2}} \, dx = 36](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B9%7D-%7Bx%5E%7B2%7D%7D%20%5C%2C%20dx%20%3D%2036)
Step-by-step explanation:
The equations are:
![y = x^{2} + 2x + 3](https://tex.z-dn.net/?f=y%20%3D%20x%5E%7B2%7D%20%2B%202x%20%2B%203)
![y = 2x + 12](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%2012)
The two graphs intersect when:
![x^{2} + 2x + 3 = 2x + 12](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%202x%20%2B%203%20%3D%202x%20%2B%2012)
![x^{2} = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D%200)
![x_{1} = 3\\x_{2} = -3](https://tex.z-dn.net/?f=x_%7B1%7D%20%20%3D%203%5C%5Cx_%7B2%7D%20%20%3D%20-3)
To find the area under the curve for the first equation:
![A_{1} = \int\limits^3__-3}{x^{2} + 2x + 3} \, dx](https://tex.z-dn.net/?f=A_%7B1%7D%20%3D%20%5Cint%5Climits%5E3__-3%7D%7Bx%5E%7B2%7D%20%2B%202x%20%2B%203%7D%20%5C%2C%20dx)
To find the area under the curve for the second equation:
![A_{2} = \int\limits^3__-3}{2x + 12} \, dx](https://tex.z-dn.net/?f=A_%7B2%7D%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B2x%20%2B%2012%7D%20%5C%2C%20dx)
To find the total area:
![A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx](https://tex.z-dn.net/?f=A%20%3D%20A_%7B2%7D%20-A_%7B1%7D%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B2x%20%2B%2012%7D%20%5C%2C%20dx%20-%5Cint%5Climits%5E3__-3%7D%7Bx%5E%7B2%7D%20%2B%202x%20%2B%203%7D%20%5C%2C%20dx)
Simplifying the equation:
![A = \int\limits^3__-3}{2x + 12}-({x^{2} + 2x + 3}) \, dx = \int\limits^3__-3}{9}-{x^{2}} \, dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B2x%20%2B%2012%7D-%28%7Bx%5E%7B2%7D%20%2B%202x%20%2B%203%7D%29%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B9%7D-%7Bx%5E%7B2%7D%7D%20%5C%2C%20dx)
Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).