Mathematics, 30.03.2020 23:25, lazymarshmallow7
The length s(t)s(t)s, (, t, )of the side of the base of a square prism is decreasing at a rate of 777 kilometers per minute and the height h(t)h(t)h, (, t, )of the prism is increasing at a rate of 101010 kilometers per minute. At a certain instant t_0t 0 t, start subscript, 0, end subscript, the base's side is 444 kilometers and the height is 999 kilometers. What is the rate of change of the surface area A(t)A(t)A, (, t, )of the prism at that instant?
Answers: 2
![A_{s} (t) = 4\cdot l(t)\cdot h(t) + 2\cdot [l(t)]^{2}](/tpl/images/0571/8210/f44e5.png)
![\frac{dA_{s}}{dt} = 4\cdot [h(t)\cdot \frac{dl}{dt} + l(t)\cdot \frac{dh}{dt}] + 2\cdot l(t)\cdot \frac{dl}{dt}](/tpl/images/0571/8210/f0b10.png)
![\frac{dA_{s}}{dt} = 4\cdot [(9\,km)\cdot (-7\,\frac{km}{min} )+(4\,km)\cdot (10\,\frac{km}{min} )] + 2\cdot (4\,km)\cdot (-7\,\frac{km}{min} )](/tpl/images/0571/8210/01d5b.png)
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The length s(t)s(t)s, (, t, )of the side of the base of a square prism is decreasing at a rate of 77...
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