Determine whether the number is rational or irrational and round it to the nearest hundredth. - 3/7
2 answers:
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For this case we have to:
x: Let the variable representing the number of people to travel in the group
y: Let the variable representing the number of miles traveled.
If friends only have $22 then we have the following inequality:
Now, if there are three people in the group we have that
The taxi can travel a maximum of 19.33 miles.
On the other hand, if the group wants to travel 10 miles then we have to y = 10.
Thus, they could travel a maximum of 5 people.
ANswer:
Traveling 3 people, the taxi can travel a maximum of 19.33 miles
Traveling 10 miles, a maximum of 5 people can travel
The first limit is known as a left-hand limit. We're approaching x = 3 from the left. This means we start with values smaller than x = 3, say x = 2.5 and move closer to x = 3.
Because x is starting off smaller than 3, we use the first piece of the piecewise function. This is the piece that corresponds to x < 3. So we plug x = 3 into that piece to get
2x^2 - x = 2(3)^2 - 3 = 2(9) - 3 = 18 - 3 = 15
So the result for the left-hand limit is 15.
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The right hand limit will have us start on the other side of x = 3. We start at x = 3.5 and move closer to x = 3. So we'll use the
portion.
Plug x = 3 into the second piece to get
3 - x = 3 - 3 = 0
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The result of the left-hand limit was 15
The result of the right-hand limit was 0
The fact that the results do not match up means that the overall limit at x = 3 does NOT exist.
Because x is starting off smaller than 3, we use the first piece of the piecewise function. This is the piece that corresponds to x < 3. So we plug x = 3 into that piece to get
2x^2 - x = 2(3)^2 - 3 = 2(9) - 3 = 18 - 3 = 15
So the result for the left-hand limit is 15.
----------------------------------------------------------
The right hand limit will have us start on the other side of x = 3. We start at x = 3.5 and move closer to x = 3. So we'll use the
Plug x = 3 into the second piece to get
3 - x = 3 - 3 = 0
--------------------------------------------------------------------------
The result of the left-hand limit was 15
The result of the right-hand limit was 0
The fact that the results do not match up means that the overall limit at x = 3 does NOT exist.