Question

Question 2 of 10

2 Points
The temperature is 45°F. The temperature will decrease by 2°F each hour. Let
h be the number of hours.
When will the temperature be below 32°F?
Write an inequality for this problem.
O
A. 45 + 2h 32
B. 45 + 2h< 32
O c. 45 - 2h<32
O
D. 45 - 2hs 32​

Answer 1

45-2(h-1)<32

Explanation:

This is a problem related to arithmetic progression. The formula we use is that of for nth term

`a_(n)=a+(n-1)d`

Here

`a=45 , d=-2 ,n=h , a_(n)=a_(h)`

`a_(h)=45+(h-1)(-2)\\a_(h)=45-2(h-1)\\`

Now we have to analyse a situation when our temperature comes below 32

or

`a_(h)<32[tex]</p><p>[tex]45-2(h-1)<32\\45-2h+2<32\\45-2h<32-2\\45-2h<30\\`

This is our inequality

Solving this

`45-2h<30\\-2h<30-45\\-2h<-15\\h>7.5\\`

Hence in 8th hours the temperature will be below 32F