So, the task: The volume of fuel in a tank changes at a rate given by the equation V ′ ( t ) = 4 t t 2 + 3 3 ≥ 0At t = [ d ] hours the tank holds 9. [ b ] gallons. What is the volume of fuel inthe tank after [ c ] hours? Round answer to one decimal place.

Question

So, the task: The volume of fuel in a tank changes at a rate given by the equation       V    ′    (  t  )  =            4      t                                t                      2                          +        3            3        ≥  0At   t  =      [    d    ]   hours the tank holds   9.  [  b  ] gallons. What is the volume of fuel inthe tank after   [  c  ] hours? Round answer to one decimal place.

hutchman420OG8 · Accepted Answer

V    ′    (  t  )  =            4      t                                t                      2                          +        3            3        ⇒            d      v              d      t        =            4      t                                t                      2                          +        3            3        ⇒  d  v  =            4      t      d      t                                t                      2                          +        3            3        V  =  ∫            4      t      d      t                                t                      2                          +        3            3        +  cTake       t          2        +  3  =  u  ⇒  2  t  d  t  =  d  u  ⇒  △  t  d  t  =  2  d  u  V  =  ∫            2      d      u              u      3        =  ∫      u                            −          1                3              d  u  =            2              u                                            −              1                        3                    +          1                                              −          1                3            +      1        =  3      u                  2        3              ⇒  V  (  t  )  =  3  (      t          2      +      3            )                  2        3              +  cGiven,  V  (      9    )  =  9  ⋅  5  ⇒  V  (  3  )  =  9  ⋅  5  ⇒  3  (  12      )                  2        3              +  c  =  9  ⋅  5  ⇒  c  =  9  ⋅  5  −  3  ×      12                  2        3              ⇒  c  =  −  6  ⋅  2  V  (  t  )  =  3  (      t          2        +  3      )                  2        3              −  6  ⋅  2  V  (  7  )  =  3  (      7          2        +  3      )                  2        3              −  6  ⋅  2  =  35  ⋅  6  g  a  l

So, the task: The volume of fuel in a tank changes at a rate given by the equation V′(t)=4t/root(3)(t^2+3)=>0 At t=sqrt[d] hours the tank holds 9.[b] gallons. What is the volume of fuel in the tank after [c] hours? Round answer to one decimal place.

Answered question

Answer & Explanation

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