For the following exercises, find the slope of a tangent line to a polar curve r = f ( θ ) . Let x = r cos θ = f ( θ ) cos θ and y = r sin θ = f ( θ ) sin θ , so the polar equation r = f ( θ ) is now written in parametric form. 236. r = 1 − sin θ ; ( 1 2 , π 6 )
For the following exercises, find the slope of a tangent line to a polar curve r = f ( θ ) . Let x = r cos θ = f ( θ ) cos θ and y = r sin θ = f ( θ ) sin θ , so the polar equation r = f ( θ ) is now written in parametric form. 236. r = 1 − sin θ ; ( 1 2 , π 6 )
For the following exercises, find the slope of a tangent line to a polar curve
r
=
f
(
θ
)
. Let
x
=
r
cos
θ
=
f
(
θ
)
cos
θ
and
y
=
r
sin
θ
=
f
(
θ
)
sin
θ
, so the polar equation
r
=
f
(
θ
)
is now written in parametric form.
Suppose an experiment was conducted to compare the mileage(km) per litre
obtained by competing brands of petrol I,II,III. Three new Mazda, three new
Toyota and three new Nissan cars were available for experimentation. During the
experiment the cars would operate under same conditions in order to eliminate
the effect of external variables on the distance travelled per litre on the assigned
brand of petrol. The data is given as below:
Brands of Petrol Mazda Toyota Nissan
I 10.6 12.0 11.0
II 9.0 15.0 12.0
III 12.0 17.4 13.0
(a) Test at the 5% level of significance whether there are signi
cant differences among the brands of fuels and also among the cars. [10]
(b) Compute the standard error for comparing any two fuel brands means. Hence
compare, at the 5% level of significance, each of fuel brands II, and III with
the standard fuel brand I. [10]
Business discuss
Use the method of undetermined coefficients to solve the given nonhomogeneous system.X' =
−1 33 −1
X +
−4t2t + 2
X(t) =
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