Respuesta :
Answer:
According to the information of the problem x = 15 , p=2.90 and dp/dt = -1.15
then [tex]\frac{dx}{dt} = -3.357\\[/tex]
Step-by-step explanation:
Since everything is changing with respect to time and [tex]p,x[/tex] are related according to the following equation
[tex]5p+5x+3px = 71[/tex]
We need to find the implicit derivative with respect to the time. And we get the following.
[tex]5\frac{dp}{dt}+5\frac{dx}{dt}+3x\frac{dp}{dt}+3p\frac{dx}{dt} = 0[/tex]
[tex]\frac{dx}{dt}[/tex] is what we don't know, so we solve for it and get
[tex]\frac{dx}{dt} = - (5\frac{dp}{dt}-3x\frac{dp}{dt})/ (5+3p)[/tex]
Now. According to the information of the problem x = 15 , p=2.90 and dp/dt = -1.15
then [tex]\frac{dx}{dt} = -3.357\\[/tex]
