tangent
Not Supported
p
=
-
x
±
x
x0
-
4
(
x1
)
(
x2
x3
-
y
)
2
(
-
g
x
2
x4
)
Search
Returned 96 matches (100 formulae, 79 docs)
Lookup 118.124 ms, Re-ranking 1497.530 ms
Found 582319 tuple postings, 151008 formulae, 20150 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
p
=
-
x
±
x
2
-
4
(
-
g
x
2
2
v
2
)
(
-
g
x
2
2
v
2
-
y
)
2
(
-
g
x
2
2
v
2
)
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
x
=
-
b
±
b
2
-
4
a
c
2
a
⇒
x
=
y
2
y
1
=
-
1
2
±
1
2
2
-
4
(
1
2
)
(
-
F
r
1
2
)
2
(
1
2
)
=
-
1
2
±
1
4
+
2
F
r
1
2
1
Doc 2
0.4660, -55.0000, 12.0000, 0.6340
testing/wikipedia/v3/27191.html
x
=
-
1
2
±
(
1
/
2
)
2
-
4
(
1
/
2
)
(
F
r
1
2
)
2
(
1
/
2
)
=
-
1
2
(
1
/
4
)
-
8
(
F
r
1
2
)
.
Doc 3
0.4416, -34.0000, 11.0000, 0.4416
testing/wikipedia/v3/27176.html
f
′′
(
x
)
=
(
q
p
)
(
q
p
-
1
)
x
q
p
-
2
Doc 4
0.2979, -12.0000, 4.0000, 0.2979
testing/wikipedia/v3/00467.html
R
i
-
(
1
+
i
)
n
(
R
i
-
P
)
Doc 5
0.2821, -7.0000, 4.0000, 0.2821
testing/wikipedia/v3/12489.html
Z
P
=
b
h
2
4
-
(
b
-
2
t
)
(
h
2
-
t
)
2
Doc 6
0.2821, -13.0000, 4.0000, 0.2821
testing/wikipedia/v3/21772.html
p
=
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
θ
=
arctan
(
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
)
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
θ
=
tan
-
1
(
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
)
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
∫
0
∞
ϕ
(
a
x
)
Φ
(
b
x
)
d
x
=
(
2
π
a
)
-
1
(
π
2
-
arctan
(
b
a
)
)
Doc 7
0.2595, -22.0000, 4.0000, 0.2595
testing/wikipedia/v3/26436.html
z
=
1
2
(
x
2
+
y
2
)
(
1
a
2
-
1
b
2
)
+
x
y
(
1
a
2
+
1
b
2
)
Doc 8
0.2595, -26.0000, 4.0000, 0.2595
testing/wikipedia/v3/02322.html
1
f
=
(
n
-
1
)
(
1
R
1
-
1
R
2
)
.
Doc 9
0.2442, -12.0000, 4.0000, 0.2442
testing/wikipedia/v3/00892.html
β
^
=
(
1
-
x
¯
)
(
x
¯
(
1
-
x
¯
)
v
¯
-
1
)
,
Doc 10
0.2442, -15.0000, 4.0000, 0.2442
testing/wikipedia/v3/02956.html
I
R
R
=
(
InvoicePrice
PurchasePriceOfBond
-
1
)
(
dayBase
daysToDelivery
)
Doc 11
0.2208, -7.0000, 3.0000, 0.2208
testing/wikipedia/v3/22711.html
Δ
=
2
(
K
N
-
p
)
Doc 12
0.2062, -3.0000, 3.0000, 0.2062
testing/wikipedia/v3/11554.html
(
p
+
r
2
)
(
q
+
s
2
)
Doc 13
0.2062, -6.0000, 3.0000, 0.2062
testing/wikipedia/v3/03760.html
=
(
3
331
)
(
5
331
)
(
161
331
)
Doc 14
0.2062, -7.0000, 3.0000, 0.8247
testing/wikipedia/v3/00617.html
=
(
3
331
)
(
5
331
)
(
823
331
)
Doc 14
0.2062, -7.0000, 3.0000, 0.8247
testing/wikipedia/v3/00617.html
(
p
-
1
2
)
(
q
-
1
2
)
,
Doc 15
0.2062, -7.0000, 3.0000, 0.2062
testing/wikipedia/v3/11626.html
concentration of cells in original mixture
=
(
number of cells counted
(
proportion of chamber counted
)
(
volume of chamber
)
)
(
volume of sample dilution
volume of original mixture in sample
)
Doc 16
0.2062, -7.0000, 3.0000, 0.2062
testing/wikipedia/v3/05323.html
v
max
=
2
(
P
atm
ρ
-
g
h
B
)
Doc 20
0.2062, -8.0000, 3.0000, 0.2062
testing/wikipedia/v3/04967.html
(
a
n
m
)
=
(
a
n
)
(
a
m
)
Doc 19
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/06302.html
(
a
m
n
)
=
(
a
m
)
(
a
n
)
Doc 17
0.2062, -8.0000, 3.0000, 0.6186
testing/wikipedia/v3/02166.html
(
0.5036
mol Ag
1
)
(
107.87
g Ag
1
mol Ag
)
=
54.32
g Ag
Doc 18
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/00980.html
(
0.2518
mol Cu
1
)
(
2
mol Ag
1
mol Cu
)
=
0.5036
mol Ag
Doc 18
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/00980.html
(
a
b
n
)
=
(
a
n
)
(
b
n
)
Doc 17
0.2062, -8.0000, 3.0000, 0.6186
testing/wikipedia/v3/02166.html
Doc 19
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/06302.html
(
a
b
p
)
=
(
a
p
)
(
b
p
)
.
Doc 14
0.2062, -7.0000, 3.0000, 0.8247
testing/wikipedia/v3/00617.html
(
v
c
)
2
(
r
r
s
-
1
)
=
1
2
.
Doc 21
0.2062, -11.0000, 4.0000, 0.3359
testing/wikipedia/v3/02950.html
(
p
q
)
4
(
q
p
)
4
=
(
2
q
)
s
.
Doc 23
0.2062, -11.0000, 3.0000, 0.4124
testing/wikipedia/v3/23225.html
(
α
𝔭
)
n
(
β
𝔭
)
n
=
(
α
β
𝔭
)
n
Doc 22
0.2062, -11.0000, 3.0000, 0.6186
testing/wikipedia/v3/28112.html
(
α
β
π
)
3
=
(
α
π
)
3
(
β
π
)
3
Doc 24
0.2062, -11.0000, 3.0000, 0.2062
testing/wikipedia/v3/14686.html
=
(
3
331
)
(
5
331
)
(
7
331
)
(
23
331
)
Doc 14
0.2062, -7.0000, 3.0000, 0.8247
testing/wikipedia/v3/00617.html
(
1001
9907
)
=
(
7
9907
)
(
11
9907
)
(
13
9907
)
.
Doc 17
0.2062, -8.0000, 3.0000, 0.6186
testing/wikipedia/v3/02166.html
(
a
n
)
(
a
i
n
)
=
(
a
⋅
a
i
n
)
,
Doc 25
0.2062, -12.0000, 3.0000, 0.2062
testing/wikipedia/v3/07259.html
(
α
𝔞
)
n
(
α
𝔟
)
n
=
(
α
𝔞
𝔟
)
n
.
Doc 22
0.2062, -11.0000, 3.0000, 0.6186
testing/wikipedia/v3/28112.html
log
(
G
(
1
2
+
z
)
G
(
1
2
-
z
)
)
=
Doc 26
0.2062, -12.0000, 3.0000, 0.2062
testing/wikipedia/v3/09909.html
(
α
𝔞
)
n
(
β
𝔞
)
n
=
(
α
β
𝔞
)
n
.
Doc 22
0.2062, -11.0000, 3.0000, 0.6186
testing/wikipedia/v3/28112.html
0.7
e
-
(
.1
)
(
3
12
)
+
0.7
e
-
(
.1
)
(
5
12
)
=
1.3541
Doc 27
0.2062, -16.0000, 3.0000, 0.2062
testing/wikipedia/v3/27993.html
∑
x
sinh
a
x
=
1
2
csch
(
a
2
)
cosh
(
a
2
-
a
x
)
+
C
Doc 28
0.2062, -18.0000, 3.0000, 0.2062
testing/wikipedia/v3/23915.html
(
p
q
)
4
(
q
p
)
4
=
(
-
1
)
f
g
2
(
-
1
e
)
.
Doc 23
0.2062, -11.0000, 3.0000, 0.4124
testing/wikipedia/v3/23225.html
0
=
-
g
x
2
2
v
2
p
2
+
x
p
-
g
x
2
2
v
2
-
y
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
(
∂
∂
t
+
V
g
→
⋅
∇
)
(
-
∂
Φ
∂
p
)
-
σ
ω
=
k
J
p
Doc 29
0.2062, -20.0000, 3.0000, 0.2062
testing/wikipedia/v3/27621.html
0
=
-
g
x
2
2
v
2
tan
2
θ
+
x
tan
θ
-
g
x
2
2
v
2
-
y
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
F
(
ε
)
=
ε
2
∫
0
1
(
2
u
-
ln
(
1
u
)
-
2
)
e
-
ε
u
d
u
Doc 30
0.2062, -24.0000, 3.0000, 0.2062
testing/wikipedia/v3/28186.html
y
3
=
(
x
1
2
+
y
1
2
-
2
(
x
1
)
2
-
4
(
y
1
2
-
1
)
y
1
2
+
(
x
1
2
-
y
1
2
)
2
y
1
=
0
Doc 31
0.2062, -37.0000, 2.0000, 0.2062
testing/wikipedia/v3/25062.html
ζ
Ai
(
1
)
=
-
3
-
2
/
3
Γ
(
2
3
)
Γ
(
4
3
)
.
Doc 32
0.1931, -16.0000, 5.0000, 0.1931
testing/wikipedia/v3/25445.html
log
(
a
T
)
=
E
a
R
(
1
T
-
1
T
0
)
Doc 33
0.1818, -12.0000, 3.0000, 0.1818
testing/wikipedia/v3/21110.html
x
(
t
)
=
2
(
t
a
-
⌊
1
2
+
t
a
⌋
)
Doc 34
0.1818, -13.0000, 4.0000, 0.3499
testing/wikipedia/v3/01650.html
(
d
u
d
φ
)
2
=
1
b
2
-
(
1
-
u
r
s
)
(
1
a
2
+
u
2
)
Doc 35
0.1818, -21.0000, 3.0000, 0.1818
testing/wikipedia/v3/08386.html
ϕ
(
p
)
=
(
x
0
ℏ
π
)
1
/
2
⋅
exp
(
-
x
0
2
(
p
-
p
0
)
2
2
ℏ
2
)
,
Doc 36
0.1818, -26.0000, 4.0000, 0.1818
testing/wikipedia/v3/01067.html
(
∂
T
∂
P
)
V
(
∂
S
∂
V
)
P
Doc 37
0.1681, -9.0000, 3.0000, 0.3361
testing/wikipedia/v3/06999.html
-
(
∂
T
∂
V
)
P
(
∂
S
∂
P
)
V
Doc 37
0.1681, -9.0000, 3.0000, 0.3361
testing/wikipedia/v3/06999.html
=
2
(
t
a
-
floor
(
1
2
+
t
a
)
)
Doc 34
0.1818, -13.0000, 4.0000, 0.3499
testing/wikipedia/v3/01650.html
(
∂
z
∂
x
)
y
(
∂
x
∂
z
)
y
=
1.
Doc 38
0.1681, -11.0000, 3.0000, 0.3361
testing/wikipedia/v3/04601.html
(
1
)
(
∂
𝐱
∂
𝐗
)
T
⋅
(
∂
𝐱
∂
𝐗
)
=
𝑪
Doc 39
0.1681, -13.0000, 3.0000, 0.1681
testing/wikipedia/v3/25135.html
x
(
t
)
=
|
2
(
t
a
-
⌊
t
a
+
1
2
⌋
)
|
Doc 40
0.1681, -15.0000, 3.0000, 0.1681
testing/wikipedia/v3/01651.html
W
q
(
H
)
=
λ
(
1
λ
2
+
σ
B
2
)
2
(
1
-
ρ
)
.
Doc 41
0.1681, -17.0000, 4.0000, 0.1681
testing/wikipedia/v3/28067.html
(
∂
z
∂
x
)
y
=
-
(
∂
z
∂
y
)
x
(
∂
y
∂
x
)
z
Doc 42
0.1681, -18.0000, 3.0000, 0.1681
testing/wikipedia/v3/14685.html
(
8
)
(
∂
z
∂
y
)
x
=
-
(
∂
z
∂
x
)
y
(
∂
x
∂
y
)
z
Doc 38
0.1681, -11.0000, 3.0000, 0.3361
testing/wikipedia/v3/04601.html
M
x
=
(
-
x
4
2
+
4
x
3
3
-
20
x
2
+
80
x
)
|
0
2
Doc 43
0.1681, -20.0000, 3.0000, 0.1681
testing/wikipedia/v3/11687.html
q
2
g
(
1
y
1
-
1
y
2
)
=
1
2
(
y
2
2
-
y
1
2
)
Doc 2
0.4660, -55.0000, 12.0000, 0.6340
testing/wikipedia/v3/27191.html
q
2
g
(
1
y
1
-
1
y
2
)
=
1
2
(
y
z
2
-
y
1
2
)
Doc 44
0.1681, -21.0000, 3.0000, 0.1681
testing/wikipedia/v3/26075.html
=
-
-
2
α
(
2
π
)
d
/
2
(
d
2
)
!
(
1
2
F
)
d
/
2
,
Doc 46
0.1681, -21.0000, 3.0000, 0.1681
testing/wikipedia/v3/10974.html
|
x
-
1
2
(
a
c
+
b
d
)
|
=
1
2
(
b
d
-
a
c
)
Doc 45
0.1681, -21.0000, 3.0000, 0.1681
testing/wikipedia/v3/27724.html
1
(
u
+
A
)
(
u
-
A
)
=
1
2
A
(
1
u
-
A
-
1
u
+
A
)
Doc 47
0.1681, -22.0000, 3.0000, 0.1681
testing/wikipedia/v3/05353.html
det
(
∂
∂
z
-
L
(
z
)
)
=
∑
i
=
0
n
H
i
(
z
)
(
∂
∂
z
)
i
.
Doc 48
0.1681, -22.0000, 3.0000, 0.1681
testing/wikipedia/v3/23866.html
f
=
v
2
(
ℓ
L
x
)
2
+
(
m
L
y
)
2
+
(
n
L
z
)
2
Doc 49
0.1519, -20.0000, 3.0000, 0.1519
testing/wikipedia/v3/12330.html
x
=
3
λ
2
1
3
-
(
ϕ
π
)
2
Doc 50
0.1422, -11.0000, 3.0000, 0.1422
testing/wikipedia/v3/17620.html
S
N
(
f
)
=
N
0
2
(
1
+
(
w
B
)
2
)
Doc 51
0.1422, -12.0000, 2.0000, 0.1422
testing/wikipedia/v3/06533.html
tan
A
=
(
(
-
∂
z
∂
y
)
(
∂
z
∂
x
)
)
Doc 52
0.1422, -13.0000, 3.0000, 0.1422
testing/wikipedia/v3/00438.html
d
y
d
x
=
-
4
x
3
4
y
=
-
x
3
y
Doc 53
0.1422, -14.0000, 3.0000, 0.1422
testing/wikipedia/v3/03420.html
∫
(
x
2
2
+
y
x
)
d
y
=
y
x
2
2
+
x
y
2
2
Doc 54
0.1422, -18.0000, 4.0000, 0.1422
testing/wikipedia/v3/04191.html
λ
=
1
2
(
-
b
m
±
b
2
m
2
-
4
ω
0
2
)
.
Doc 55
0.1422, -18.0000, 3.0000, 0.1422
testing/wikipedia/v3/04432.html
d
d
x
(
1
x
3
+
4
x
)
=
-
3
x
2
-
4
(
x
3
+
4
x
)
2
.
Doc 56
0.1422, -23.0000, 4.0000, 0.2719
testing/wikipedia/v3/13099.html
1
2
(
x
2
-
4
x
+
2
)
Doc 57
0.1297, -7.0000, 3.0000, 0.1297
testing/wikipedia/v3/07059.html
(
p
1
-
x
(
1
-
p
)
)
r
Doc 58
0.1297, -7.0000, 2.0000, 0.1297
testing/wikipedia/v3/19303.html
ψ
1
(
3
2
)
=
π
2
2
-
4
Doc 59
0.1297, -9.0000, 2.0000, 0.1297
testing/wikipedia/v3/09858.html
x
=
p
2
+
(
p
2
)
2
-
q
Doc 60
0.1297, -10.0000, 3.0000, 0.1297
testing/wikipedia/v3/00855.html
f
(
x
)
=
x
3
-
2
x
2
(
x
2
-
5
)
Doc 61
0.1297, -12.0000, 4.0000, 0.1297
testing/wikipedia/v3/04272.html
sin
(
x
2
)
=
±
1
2
(
1
-
cos
x
)
Doc 62
0.1297, -12.0000, 2.0000, 0.1297
testing/wikipedia/v3/02375.html
ξ
=
1
2
(
R
I
R
-
R
R
I
)
sin
β
Doc 63
0.1297, -13.0000, 3.0000, 0.1297
testing/wikipedia/v3/22312.html
E
(
z
)
=
exp
[
-
4
(
(
z
-
z
0
)
I
c
)
2
]
Doc 66
0.1297, -14.0000, 3.0000, 0.1297
testing/wikipedia/v3/27921.html
X
=
1
2
[
(
T
β
)
0.5
-
(
T
β
)
-
0.5
]
Doc 64
0.1297, -14.0000, 3.0000, 0.1297
testing/wikipedia/v3/21706.html
η
p
=
2
(
v
v
e
)
1
+
(
v
v
e
)
2
Doc 65
0.1297, -14.0000, 3.0000, 0.1297
testing/wikipedia/v3/00547.html
Cl
2
(
π
4
)
-
Cl
2
(
3
π
4
)
=
G
2
Doc 67
0.1297, -14.0000, 2.0000, 0.1297
testing/wikipedia/v3/04615.html
r
r
s
(
v
c
)
2
(
1
-
r
s
r
)
=
1
2
Doc 21
0.2062, -11.0000, 4.0000, 0.3359
testing/wikipedia/v3/02950.html
(
J
0
3
f
)
(
x
)
=
-
x
-
x
2
2
-
x
3
3
Doc 68
0.1297, -16.0000, 2.0000, 0.1297
testing/wikipedia/v3/08705.html
ω
±
=
ω
c
2
±
(
ω
c
2
)
2
-
ω
t
2
2
Doc 69
0.1297, -17.0000, 3.0000, 0.1297
testing/wikipedia/v3/10151.html
f
(
x
)
=
1
+
2
(
1
x
+
x
x
2
-
4
x
+
8
)
Doc 70
0.1297, -17.0000, 3.0000, 0.1297
testing/wikipedia/v3/03370.html
e
=
(
x
0
-
x
)
2
+
(
y
0
-
y
)
2
2
a
(
17
)
Doc 71
0.1297, -17.0000, 3.0000, 0.1297
testing/wikipedia/v3/23312.html
d
d
x
(
1
g
(
x
)
)
=
-
g
′
(
x
)
(
g
(
x
)
)
2
Doc 56
0.1422, -23.0000, 4.0000, 0.2719
testing/wikipedia/v3/13099.html
y
=
R
(
2
(
x
L
)
-
K
′
(
x
L
)
2
2
-
K
′
)
Doc 72
0.1297, -18.0000, 3.0000, 0.1297
testing/wikipedia/v3/09114.html
1
+
2
(
1
8
)
+
4
(
1
8
)
2
+
8
(
1
8
)
3
+
⋯
.
Doc 74
0.1297, -20.0000, 3.0000, 0.1297
testing/wikipedia/v3/00449.html
1
+
7
x
+
12
x
2
-
4
x
3
(
1
-
x
2
)
(
1
-
16
x
2
)
Doc 73
0.1297, -20.0000, 3.0000, 0.2310
testing/wikipedia/v3/24194.html
ln
(
p
(
z
2
)
p
(
z
1
)
)
=
-
g
R
⋅
T
¯
(
z
2
-
z
1
)
Doc 75
0.1297, -21.0000, 3.0000, 0.1297
testing/wikipedia/v3/16091.html
Area
=
T
+
2
(
T
8
)
+
4
(
T
8
2
)
+
8
(
T
8
3
)
+
⋯
.
Doc 76
0.1297, -22.0000, 3.0000, 0.1297
testing/wikipedia/v3/17742.html
π
x
2
6
-
3
x
2
-
(
x
2
)
2
2
+
x
2
-
(
x
2
)
2
2
Doc 77
0.1297, -26.0000, 3.0000, 0.1297
testing/wikipedia/v3/00025.html
V
=
m
2
(
g
L
a
x
a
2
+
g
L
b
x
b
2
+
k
m
(
x
b
-
x
a
)
2
)
.
Doc 78
0.1297, -29.0000, 3.0000, 0.1297
testing/wikipedia/v3/08199.html
1
(
1
-
x
)
(
1
-
4
x
)
Doc 73
0.1297, -20.0000, 3.0000, 0.2310
testing/wikipedia/v3/24194.html
p
=
∂
g
∂
z
(
∂
g
∂
x
)
2
+
(
∂
g
∂
y
)
2
Doc 79
0.1013, -20.0000, 3.0000, 0.1013
testing/wikipedia/v3/25915.html