Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. Let R be the unit disk centered at (0,0). Then ∬ R ( x 2 + y 2 ) d A = ∫ 0 2 π ∫ 0 1 r 2 d r d θ . b. The average distance between the points of the hemisphere z = 4 − x 2 − y 2 and the origin is 2 (calculus not required). c. The integral ∫ 0 1 ∫ 0 1 − y 2 e x 2 + y 2 d x d y is easier to evaluate in polar coordinates than in Cartesian coordinates.
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. Let R be the unit disk centered at (0,0). Then ∬ R ( x 2 + y 2 ) d A = ∫ 0 2 π ∫ 0 1 r 2 d r d θ . b. The average distance between the points of the hemisphere z = 4 − x 2 − y 2 and the origin is 2 (calculus not required). c. The integral ∫ 0 1 ∫ 0 1 − y 2 e x 2 + y 2 d x d y is easier to evaluate in polar coordinates than in Cartesian coordinates.
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. Let R be the unit disk centered at (0,0). Then
∬
R
(
x
2
+
y
2
)
d
A
=
∫
0
2
π
∫
0
1
r
2
d
r
d
θ
.
b. The average distance between the points of the hemisphere
z
=
4
−
x
2
−
y
2
and the origin is 2 (calculus not required).
c. The integral
∫
0
1
∫
0
1
−
y
2
e
x
2
+
y
2
d
x
d
y
is easier to evaluate in polar coordinates than in Cartesian coordinates.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
i.
45
i.
654
111.
545
iv.
665
V.
6565
Use nl= 0401 and let n2 = 45. Using Fibonacci series, generate the values
of n3 up to n10. Do this for i., ii, iv and v.
Suppose you are asked to design a rotating disk where the number of bits per track is constant. You know that the number of bits per track is determined by the circumference of the innermost track, which you can assume is also the circumference of the hole. Thus, if you make the hole in the center of the disk larger, the number of bits per track increases, but the total number of tracks decreases. If you let r denote the radius of the platter, and x · r the radius of the hole, what value of x maximizes the capacity of the disk?
Eliminate useless variables and symbols. Afterwards, convert to Chomsky Normal Form. (Start variable S)
S -> ABBC | BA
A-> abB | aa
B -> bB | Aa
C -> Cb | aC
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