A cubic crystal is being grown as a science experiment.
a) if the sides of the crytal are increasing in size at a rate of 0.01 mm/s, how fast is the volume of the crytal increasing when its sides are 2.3 mm long?
b) if the value of the cyrstal is $4/mm^3, how fast is the value of the cyrstal increasing when its sides are 2.7 mm long?
a) ds/dt = 0.01 mm/s
dv/dt = ? when 2.3 mm
dv/ds = s^3
dv/dt = (dv/ds)(ds/dt)
= (dv/ds s^3)(0.01)
= (3 (2.3^2)(0.01)
= 0.1587
b) dc/ds = 4
dc/dt = ? when 2.7 mm
dc/dt = (dc/ds)(ds/dt)
= (4)(0.01)
but then there is no variable so I think I did this wrong. Can someone help me with this question? Thanks.
a) if the sides of the crytal are increasing in size at a rate of 0.01 mm/s, how fast is the volume of the crytal increasing when its sides are 2.3 mm long?
b) if the value of the cyrstal is $4/mm^3, how fast is the value of the cyrstal increasing when its sides are 2.7 mm long?
a) ds/dt = 0.01 mm/s
dv/dt = ? when 2.3 mm
dv/ds = s^3
dv/dt = (dv/ds)(ds/dt)
= (dv/ds s^3)(0.01)
= (3 (2.3^2)(0.01)
= 0.1587
b) dc/ds = 4
dc/dt = ? when 2.7 mm
dc/dt = (dc/ds)(ds/dt)
= (4)(0.01)
but then there is no variable so I think I did this wrong. Can someone help me with this question? Thanks.
