hi.............carthI
Answers
Explanation:
x=rcosθcosϕ;y=rcosθsinϕ;z=rsinθ
x
2
+y
2
+z
2
=r
2
.
x
2
=r
2
cos
2
θcos
2
ϕ
y
2
=r
2
cos
2
θsin
2
ϕ
z
2
=r
2
sin
2
θ.
r
2
cos
2
θcos
2
ϕ+r
2
cos
2
θsin
2
ϕ+r
2
sin
2
θ=r
2
r
2
(cos
2
θcos
2
ϕ+cos
2
θsin
2
ϕ+sin
2
θ)=r
2
r
2
[cos
2
θ(sin
2
ϕ+cos
2
ϕ)+sin
2
θ]=r
2
r
2
[cos
2
θ(1)+sin
2
θ]=r
2
r
2
(1)=r
2
∴r
2
=r
2
∴ Hence Proved x
2
+y
2
+z
2
=r
2Totalno.ofstudents=3600
CentralangleforstudentsinScience=
3600
1000
×360=100
o
CentralangleforstudentsinCommerce=
3600
1200
×360=120
o
CentralangleforstudentsinArts=
3600
650
×360=65
o
CentralangleforstudentsinLaw=
3600
450
×360=45
o
CentralangleforstudentsinHomeScience=
3600
300
×360=30
oArrange the given data in ascending order
12,15,15,17,17,17,19,19,19,19,19,21,21,21,23,23,23,23,25,25
Frequency Distribution Table
Marks
12
15
17
19
21
23
25
No. of students
1
2
3
5
3
4
2Girls =
5
3
, Boys =(1−
5
3
)=
5
2
.
Fraction of students absent =
9
2
of
5
3
+
4
1
of
5
2
=
45
6
+
10
1
=
90
21
=
30
7
.
∴ Fraction of students present =(1−
30
7
)=
30
23
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