Question

name
date
homeroom:
ms. ordonez/ms. sparacello/ ms. brea
you try: in chicago, the temperature dropped from 21 degrees to -7 over the course of 6 hours. how many degrees did the temperature drop on average per hour?
you try: use the constraints below to determine whether the statements are always, sometimes, or never true. explain.
if p > 0 and q < 0
a. pq + pq < 0
b. pp + qq < 0
c. pqp - 1 > 0

Explanation:

Step1: Calculate total temperature drop

Find the difference between the initial and final temperatures. The initial temperature is 21 degrees and the final is - 7 degrees. So the total drop is $21-(-7)=21 + 7=28$ degrees.

Step2: Calculate average drop per hour

Divide the total temperature - drop by the number of hours. There are 6 hours, so the average drop per hour is $\frac{28}{6}=\frac{14}{3}=4\frac{2}{3}$ degrees per hour.

For the inequalities:

Part a

Step1: Simplify the left - hand side

$pq+pq = 2pq$. Since $p>0$ and $q < 0$, then $pq<0$ (a positive times a negative is negative). So $2pq<0$. The statement $pq + pq<0$ is always true.

Part b

Step1: Analyze the squares

$pp=p^{2}$ and $qq = q^{2}$. Since any non - zero real number squared is positive ($p>0$ so $p^{2}>0$ and for any $q
eq0$, $q^{2}>0$), then $p^{2}+q^{2}>0$. The statement $pp + qq<0$ is never true.

Part c

Step1: Analyze the product

$pqp=p^{2}q$. Since $p>0$, $p^{2}>0$ and $q < 0$, then $p^{2}q<0$. So $p^{2}q-1=pqp - 1< - 1<0$. The statement $pqp - 1>0$ is never true.

Answer:

The average temperature drop per hour is $4\frac{2}{3}$ degrees.
a. Always true
b. Never true
c. Never true