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

Answer:

45-2(h-1)<32

Step-by-step 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]

[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