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vesna_86 [32]
2 years ago
14

Olivia is half the age of her brother, Adam. Olivia's sister, Ava, is twice as old as Adam. Adam is 4 years old. How old is each

sibling?
Mathematics
2 answers:
AnnZ [28]2 years ago
6 0

Answer:

Step-by-step explanation:

Adam's age = 4 years

Ava's age = 2 * 4 = 8 years

Olivia's age = 4 ÷ 2  = 2 years

kiruha [24]2 years ago
3 0

Answer:

Step-by-step explanation:

Adam is 4 years old.

Ava's age = 2 * 4 = 8 years old

Olivia's age = 4 ÷ 2  = 2 years old

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Integrate <img src="https://tex.z-dn.net/?f=e%5E%7B4x%7D%5Csqrt%7B1%2Be%5E%7B2x%7D%20%7D%20dx" id="TexFormula1" title="e^{4x}\sq
AnnyKZ [126]

Answer:

(\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C

Step-by-step explanation:

<u><em> Step(i):-</em></u>

Given that the function

                    f(x) = e^{4x} \sqrt{1+e^{2x} }

Now integrating on both sides, we get

                 \int\limits{f(x)} \, dx = \int\limits{e^{4x} \sqrt{1+e^{2x} } dx

                               =    \int\limits{e^{2x} e^{2x} \sqrt{1+e^{2x} } dx

                         

<u><em>Step(ii):-</em></u>

  Let  1 + e^{2x}  = t

           e^{2x}  = t -1  

          2e^{2x}dx = d t

          e^{2x}dx = \frac{1}{2} d t

                = \int\limits{( \sqrt{1+e^{2x} }) e^{2x} e^{2x} dx

                  = \int\limits {\sqrt{t}(t-1)\frac{1}{2} dt }

                 = \frac{1}{2} \int\limits {\sqrt{t} (t) -\sqrt{t} ) dt }

                = \frac{1}{2} \int\limits {(t^{\frac{1}{2}  } t^{1} +t^{\frac{1}{2} } ) } \, dx

                = \frac{1}{2} \int\limits {(t^{\frac{3}{2}  } +t^{\frac{1}{2} } ) } \, dx

               = \frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{3}{2}+1 } + \frac{t^{\frac{1}{2} +1} }{\frac{1}{2}+1 } )+C

              =  \frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{5}{2} } + \frac{t^{\frac{1}{2} +1} }{\frac{3}{2} } )+C

             = \frac{1}{2} (\frac{t^{\frac{5}{2} } }{\frac{5}{2} } + \frac{t^{\frac{3}{2} } }{\frac{3}{2} } )+C

            = (\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C

<u><em>Final answer:-</em></u>

= (\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C

             

3 0
3 years ago
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