Answer:
y>-15/2x+10
Step-by-step explanation:
15x+2y>20
First step: Move the 15x to the other side by subtracting on both sides. 2y>-15x+20
Second step: Divide everything by 2. y>-15/2x+10
Answer:
b 33 i took test i know
Step-by-step explanation:
The ratio of growth is 26.1/25.9 = 261/259
in x years the median age = 25.9 * (261/259)^x
in 2019 (after 10 years) = 25.9 * (261/259)^10 = 27.97
Answer:
0.88 s
Step-by-step explanation:
Let x(t) be the volume of nitric acid measured in liters after t minute. Therefore the rate of change in the volume of nitric acid (dx / dt) is:
dx / dt = rate of input of nitric acid - rate of output of nitric acid
rate of input of nitric acid = 6 L/min * 20% nitric acid / 100% solution = 1.2 L/min
rate of output of nitric acid = 8 L/min * x L / 200 L = 0.04x L/min
![\frac{dx}{dt}=1.2-0.04x\\\\\frac{dx}{dt}+0.04x=1.2 \\\\The\ integrating\ factor(IF)=e^{\int\limits {0.04} \, dt }=e^{0.04t}\\\\multiply\ through\ by \ IF:\\\\e^{0.04t} \frac{dx}{t}+e^{0.04dt}(0.04x)=e^{0.04t}(1.2)\\\\integrating:xe^{0.04t}=1.2\int\limits e^{0.04t}dt\\\\xe^{0.04t}=30e^{0.04t}+C\\\\x(t)=30+Ce^{-0.04t}\\\\At\ t=0,x=1\\\\x(0)=30+Ce^{-0.04*0}\\\\1=30+C\\\\C=-29\\\\x(t)=30-29e^{-0.04t}\\\\At \ 10\%,x=10%\ of\ 200L=2\\\\2=30-29e^{-0.04t}\\\\29e^{-0.04t}=28\\\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D1.2-0.04x%5C%5C%5C%5C%5Cfrac%7Bdx%7D%7Bdt%7D%2B0.04x%3D1.2%20%5C%5C%5C%5CThe%5C%20integrating%5C%20factor%28IF%29%3De%5E%7B%5Cint%5Climits%20%7B0.04%7D%20%5C%2C%20dt%20%7D%3De%5E%7B0.04t%7D%5C%5C%5C%5Cmultiply%5C%20through%5C%20by%20%5C%20IF%3A%5C%5C%5C%5Ce%5E%7B0.04t%7D%20%5Cfrac%7Bdx%7D%7Bt%7D%2Be%5E%7B0.04dt%7D%280.04x%29%3De%5E%7B0.04t%7D%281.2%29%5C%5C%5C%5Cintegrating%3Axe%5E%7B0.04t%7D%3D1.2%5Cint%5Climits%20e%5E%7B0.04t%7Ddt%5C%5C%5C%5Cxe%5E%7B0.04t%7D%3D30e%5E%7B0.04t%7D%2BC%5C%5C%5C%5Cx%28t%29%3D30%2BCe%5E%7B-0.04t%7D%5C%5C%5C%5CAt%5C%20t%3D0%2Cx%3D1%5C%5C%5C%5Cx%280%29%3D30%2BCe%5E%7B-0.04%2A0%7D%5C%5C%5C%5C1%3D30%2BC%5C%5C%5C%5CC%3D-29%5C%5C%5C%5Cx%28t%29%3D30-29e%5E%7B-0.04t%7D%5C%5C%5C%5CAt%20%5C%2010%5C%25%2Cx%3D10%25%5C%20of%5C%20200L%3D2%5C%5C%5C%5C2%3D30-29e%5E%7B-0.04t%7D%5C%5C%5C%5C29e%5E%7B-0.04t%7D%3D28%5C%5C%5C%5C)
![29e^{-0.04t}=28\\\\e^{-0.04t}=0.9655\\\\t=0.88\ s](https://tex.z-dn.net/?f=29e%5E%7B-0.04t%7D%3D28%5C%5C%5C%5Ce%5E%7B-0.04t%7D%3D0.9655%5C%5C%5C%5Ct%3D0.88%5C%20s)
The percentage of nitric acid in the tank reach 10% at 0.88 s