Answer:
Proof in explanation.
Step-by-step explanation:
I'm going to attempt this by squeeze theorem.
We know that 
is a variable number between -1 and 1 (inclusive).
This means that 
.
for all value 
. So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.
By squeeze theorem, if
and 
, then we can also conclude that 
.
So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at 
.
.
We can finally conclude that 
by squeeze theorem.
Some people call this sandwich theorem.
Dale drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when dale drove home, there was no traffic and the trip only took 5 hours. if his average rate was 18 miles per hour faster on the trip home, how far away does dale live from the mountains? do not do any rounding.
Answer:
Dale live 315 miles from the mountains
Step-by-step explanation:
Let y be the speed of Dale to the mountains
Time taken by Dale to the mountains=7 hrs
Therefore distance covered by dale to the mountain = speed × time = 7y ......eqn 1
Time taken by Dale back home = 5hours
Since it speed increased by 18 miles per hour back home it speed = y+18
So distance traveled home =speed × time = (y+18)5 ...... eqn 2
Since distance cover is same in both the eqn 1 and eqn 2.
Eqn 1 = eqn 2
7y = (y+18)5
7y = 5y + 90
7y - 5y = 90 (collection like terms)
2y = 90
Y = 45
Substitute for y in eqn 1 to get distance away from mountain
= 7y eqn 1
= 7×45
= 315 miles.
∴ Dale leave 315 miles from the mountains
