Let
x
(
t
)
=
t
−
sin
(
t
)
\displaystyle {x}{\left({t}\right)}={t}-{\sin{{\left({t}\right)}}}
x
(
t
)
=
t
−
sin
(
t
)
and
y
(
t
)
=
1
−
cos
(
t
)
\displaystyle {\quad\text{and}\quad}{y}{\left({t}\right)}={1}-{\cos{{\left({t}\right)}}}
and
y
(
t
)
=
1
−
cos
(
t
)
All answers should be decimals
rounded to 2 decimal places.
At
t
=
5
\displaystyle {t}={5}
t
=
5
x
(
t
)
=
\displaystyle {x}{\left({t}\right)}=
x
(
t
)
=
y
(
t
)
=
\displaystyle {y}{\left({t}\right)}=
y
(
t
)
=
d
x
d
t
=
\displaystyle \frac{{{\left.{d}{x}\right.}}}{{{\left.{d}{t}\right.}}}=
d
t
d
x
=
d
y
d
t
=
\displaystyle \frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}=
d
t
d
y
=
d
y
d
x
\displaystyle \frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}
d
x
d
y
= tangent slope =
speed =
\displaystyle \text{speed =}
speed =
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