hw sec. 2.1\nscore: 10/13 answered: 10/13\nquestion 11\na company manufactures and sells cell phone cases…
hw sec. 2.1\nscore: 10/13 answered: 10/13\nquestion 11\na company manufactures and sells cell phone cases. the revenue obtained by selling e cases is given by the formula\nr = 8.4e - 0.04e²\nsolve the equation below to find the number of cell phone cases they must sell to receive $432 in revenue.\n432 = 8.4e - 0.04e²\nthey need to sell or cases to make $432 in revenue.\nquestion help: video ebook
Answer
Explanation:
Step1: Rearrange the equation
We have the quadratic - equation (0.04e^{2}-8.4e + 432 = 0). Multiply through by 100 to get rid of the decimals: (4e^{2}-840e + 43200 = 0). Then divide by 4: (e^{2}-210e + 10800 = 0).
Step2: Use the quadratic formula
The quadratic formula for (ax^{2}+bx + c = 0) is (x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}). For (e^{2}-210e + 10800 = 0), where (a = 1), (b=-210), and (c = 10800). First, calculate the discriminant (\Delta=b^{2}-4ac=(-210)^{2}-4\times1\times10800=44100 - 43200 = 900).
Step3: Find the values of e
(e=\frac{-(-210)\pm\sqrt{900}}{2\times1}=\frac{210\pm30}{2}).
- For the plus - sign: (e=\frac{210 + 30}{2}=\frac{240}{2}=120).
- For the minus - sign: (e=\frac{210 - 30}{2}=\frac{180}{2}=90).
Answer:
90, 120