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Mathematics
Mathematics
Problem
Temperature along a metal rod is given by
T
(
x
)
=
5
x
2
+
20
T(x)=5x^{2}+20
T
(
x
)
=
5
x
2
+
20
(degrees Celsius), where
x
x
x
is the distance in meters from the left end. A sensor moves so that
x
(
t
)
=
t
+
1
x(t)=\sqrt{t+1}
x
(
t
)
=
t
+
1
after
t
t
t
seconds. Calculate
d
T
d
t
\dfrac{dT}{dt}
d
t
d
T
at
t
=
3
s
t=3\text{ s}
t
=
3
s
and include appropriate units.
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