Question Solved1 Answer 7. Find the length of the path of \( c(t)=(1+2 t, 2+4 t) \) over the interval \( 1 \leq t \leq 4 \). Do this using: (a) The arc length formula. (b) High school geometry. 7. Find the length of the path of c(t)=(1+2t,2+4t) over the interval 1≤t≤4. Do this using: (a) The arc length formula. (b) High school geometry.

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Transcribed Image Text: 7. Find the length of the path of c(t)=(1+2t,2+4t) over the interval 1≤t≤4. Do this using: (a) The arc length formula. (b) High school geometry.
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Transcribed Image Text: 7. Find the length of the path of c(t)=(1+2t,2+4t) over the interval 1≤t≤4. Do this using: (a) The arc length formula. (b) High school geometry.
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{:[" (7) "C(t)=(4+2t","2+4t)quad1 <= t <= 4],[x(t)=1+2t=>x^(')(t)=2],[y(t)=2+4t quad=>y^(')(t)=4],[x=1+2t","quad y=2+4t=2(1+2t)=2x],[t=1quadquad y=2x],[x=3","y=6],[t=4","x=9","y=18],[=int_(a)^(b)sqrt((x^(1))^(2)+(y)^(2))dt],[=int_(1)^(4)sqrt(2^(2)+4^(2))dt],[ ... See the full answer