Question 2 of 102 PointsThe temperature is 45°F. The temperature will decrease by 2°F each hour. Leth be the number of hours.When will the temperature be below 32°F?Write an inequality for this problem.OA. 45 + 2h 32B. 45 + 2h< 32O c. 45 - 2h<32OD. 45 - 2hs 32
Accepted Solution
A:
Answer:45-2(h-1)<32Step-by-step explanation:This is a problem related to arithmetic progression. The formula we use is that of for nth term[tex]a_{n}=a+(n-1)d[/tex]Here [tex]a=45 , d=-2 ,n=h , a_{n}=a_{h}[/tex][tex]a_{h}=45+(h-1)(-2)\\a_{h}=45-2(h-1)\\[/tex]Now we have to analyse a situation when our temperature comes below 32or [tex]a_{h}<32[tex][tex]45-2(h-1)<32\\45-2h+2<32\\45-2h<32-2\\45-2h<30\\[/tex]This is our inequality Solving this[tex]45-2h<30\\-2h<30-45\\-2h<-15\\h>7.5\\[/tex]Hence in 8th hours the temperature will be below 32F