Ellen is currently twice as old as Maria, but in 6 years, Maria will be 2/3 as old as Ellen. How old is Ellen now?
1 answer:
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Answer:
.
In other words, the in
could be any real number as long as
for all integer
(including negative integers.)
Step-by-step explanation:
The tangent function has a real value for real inputs
as long as the input
for all integer
.
Hence, the domain of the original tangent function is .
On the other hand, in the function , the input to the tangent function is replaced with
.
The transformed tangent function would have a real value as long as its input
ensures that
for all integer
.
In other words, would have a real value as long as
.
Accordingly, the domain of would be
.
We'll use variables to represent the speeds of the eastbound and westbound trains.
x will represent the speed of the eastbound train.
y will represent the speed of the westbound train.
The eastbound train is 16 mph faster than the westbound train. An equation can be made from this:
Subtraction is used, because it represents the difference in distances between the two trains if they travel the same direction.
After 4 hours, the trains are 800 miles apart. An equation can be made from this:
Addition is used, because the trains are heading in opposite directions, which means their distances from the starting point are added together.
Set the two equations up vertically:
We will use elimination to solve for x.
Multiply the entire first equation by 4 so that the coefficients for y will be opposite numbers:
Combine the two equations together to cancel out y:
Divide both sides by 8 to get x by itself:
The speed of the eastbound train is 108 mph.
x will represent the speed of the eastbound train.
y will represent the speed of the westbound train.
The eastbound train is 16 mph faster than the westbound train. An equation can be made from this:
Subtraction is used, because it represents the difference in distances between the two trains if they travel the same direction.
After 4 hours, the trains are 800 miles apart. An equation can be made from this:
Addition is used, because the trains are heading in opposite directions, which means their distances from the starting point are added together.
Set the two equations up vertically:
We will use elimination to solve for x.
Multiply the entire first equation by 4 so that the coefficients for y will be opposite numbers:
Combine the two equations together to cancel out y:
Divide both sides by 8 to get x by itself:
The speed of the eastbound train is 108 mph.