Question 1069403
(a)
At {{{ t = 0 }}}
{{{ Q(t) = .003t^2 - .625t + 25 }}}
{{{ Q(t) = .003*0^2 - .625*0 + 25 }}}
{{{ Q(0) = 25 }}}
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(b)
{{{ Q(10) = 19.05 }}}
{{{ Q(20) = .003*20^2 - .625*20 + 25 }}}
{{{ Q(20) = .003*400 - 12.5 + 25 }}}
{{{ Q(20) = 1.2 - 12.5 + 25 }}}
{{{ Q(20) = 13.7 }}}
{{{ 13.7 - 19.05 = -5.35 }}}
units of energy used in {{{ 20 - 10 = 10 }}} min
{{{ 5.35/10 = .535 }}} average energy/min
produced for {{{ 10 <= t <= 20 }}}
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(c)
{{{ Q(t) = .003t^2 - .625t + 25 }}}
When does {{{ Q(t) = 0 }}} ?
{{{ 0 = .003t^2 - .625t + 25 }}}
Use quadratic formula
{{{ t = ( -b +- sqrt( b^2 - 4*a*c ))/(2*a) }}}
{{{ a = .003 }}}
{{{ b = -.625 }}}
{{{ c = 25 }}}
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{{{ t = ( -(-.625) +- sqrt( (-.625)^2 - 4*.003*25 ))/(2*.003) }}}
{{{ t = ( .625 +- sqrt( .3906 - .3 ))/.006 }}}
{{{ t = ( .625 +- sqrt( .0906 ))/.006 }}}
{{{ t = ( .625 + .301 ) / .006 }}}
{{{ t = .926/.006 }}}
{{{ t = 154.33 }}}
and
{{{ t = ( .625 - .301 ) / .006 }}}
{{{ t = .324/.006 }}}
{{{ t = 54 }}}
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Here's the plot:
{{{ graph( 400, 400, -5, 70, -5, 50, .003x^2 - .625x + 25 ) }}}
This tells me that at {{{ t = 54 }}} min the energy is zero
I can ignore the root {{{ t = 154.33 }}}