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skynugurq7 2022-07-03 Answered
For f ( t ) = ( e t t , 4 t + 1 t ) what is the distance between f(2) and f(5)?
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Answers (1)

gutinyalk
Answered 2022-07-04 Author has 11 answers
Step 1
We will substitute first 2 and then 5:
f ( 2 ) = ( e 2 2 , 4 2 + 1 2 ) = ( e 2 2 , 17 2 )
f ( 5 ) = ( e 5 5 , 4 5 + 1 5 ) = ( e 5 5 , 101 5 )
Step 2
Then we will apply the distance formula:
d = ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2
d = ( e 5 5 - e 2 2 ) 2 + ( 101 5 - 17 2 ) 2
= ( 2 e 5 - 5 e 2 10 ) 2 + ( 101 2 - 17 5 10 ) 2
= 4 e 10 - 20 e 7 + 25 e 4 100 + 202 - 85 100
= 4 e 10 - 20 e 7 + 25 e 4 + 117 10
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