For the following exercises, use a graphing utility to graph the curve represented by the parametric equations and identify the curve from its equation. 58. Sketch the curve known as an epitrochoid, which gives the path of a point on a circle of radius b as it rolls on the outside of a circle of radius a . The equations are x = ( a + b ) cos t − c ⋅ cos [ ( a + b ) t b ] y = ( a + b ) sin t − c ⋅ sin [ ( a + b ) t b ] Let a = 1 , b = 2 , c = 1 .
For the following exercises, use a graphing utility to graph the curve represented by the parametric equations and identify the curve from its equation. 58. Sketch the curve known as an epitrochoid, which gives the path of a point on a circle of radius b as it rolls on the outside of a circle of radius a . The equations are x = ( a + b ) cos t − c ⋅ cos [ ( a + b ) t b ] y = ( a + b ) sin t − c ⋅ sin [ ( a + b ) t b ] Let a = 1 , b = 2 , c = 1 .
For the following exercises, use a graphing utility to graph the curve represented by the parametric equations and identify the curve from its equation.
58. Sketch the curve known as an epitrochoid, which gives the path of a point on a circle of radius b as it rolls on the outside of a circle of radius a. The equations are
x
=
(
a
+
b
)
cos
t
−
c
⋅
cos
[
(
a
+
b
)
t
b
]
y
=
(
a
+
b
)
sin
t
−
c
⋅
sin
[
(
a
+
b
)
t
b
]
Why researchers are interested in describing measures of the center and measures of variation of a data set?
Let Χ be a real-valued character (mod k). Let
k
S = Σnx(n).
n=1
If (a, k) = 1,
ax(a)S = S (mod k).
(iii) Write k = 2ºq where q is odd. Show that there is an integer a
with (a, k) = 1 such that a = 3 (mod 2ª) and a = 2 (mod q).
Deduce that 12S = 0 (mod k).
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