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tilfaen4a

tilfaen4a

Answered question

2022-05-23

For f ( t ) = ( t e 1 - 3 t , 2 t 2 - t ) what is the distance between f(2) and f(5)?

Answer & Explanation

Megan Mathis

Megan Mathis

Beginner2022-05-24Added 10 answers

Step 1
We have: f ( t ) = ( t e 1 - 3 t , 2 t 2 - t )
First, let's evaluate f(2) and f(5):
f ( 2 ) = ( 2 e 1 - 3 2 , 2 2 2 - 2 )
f ( 2 ) = ( 2 e 1 - 6 , 2 4 - 2 )
f ( 2 ) = ( 2 e - 5 , 8 - 2 )
f ( 2 ) = ( 2 e 5 , 6 )
and f ( 5 ) = ( 5 e 1 - 3 5 , 2 5 2 - 5 )
f ( 5 ) = ( 5 e 1 - 15 , 2 25 - 5 )
f ( 5 ) = ( 5 e - 14 , 50 - 5 )
f ( 5 ) = ( 5 e 14 , 45 )
Step 2
Then, let's evaluate the distance between these two points:
d = ( 5 e 14 - 2 e 5 ) 2 + ( 45 - 6 ) 2
d = ( 25 e 28 - 20 e 19 + 4 e 10 ) + 39 2
d = 25 e 28 - 20 e 19 + 4 e 10 + 1521

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