Loading...
2 real liquidities
Save Copy
Desmos Logo
Log In
Sign Up
Expression 23: "b" Subscript, 1 , Baseline equals StartFraction, "L" Subscript, 1 , Baseline "c" Subscript, "r" 1 , Baseline Over StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot , EndFraction plus "L" Subscript, 1 , Baseline StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot equals 4.8 3 6 6 5 4 2 4 0 3 7
b
1
=
L
1
c
r
1
p
b
1
+
L
1
p
a
1
equals
=
4.8 3 6 6 5 4 2 4 0 3 7
4
.
8
3
6
6
5
4
2
4
0
3
7
23
Expression 24: "c" Subscript, 1 , Baseline equals negative "L" squared left parenthesis, 1 minus StartFraction, StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot Over StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot , EndFraction , right parenthesis equals negative 4.5
c
1
=
−
L
2
1
1
−
p
a
1
p
b
1
equals
=
negative 4.5
−
4
.
5
24
Expression 25: "x" Subscript, "r" 1 , Baseline equals StartFraction, negative "b" Subscript, 1 , Baseline positive StartRoot, "b" squared minus 4 "a" Subscript, 1 , Baseline "c" Subscript, 1 , Baseline , EndRoot Over 2 "a" Subscript, 1 , Baseline , EndFraction equals 0.7 7 2 4 7 4 2 1 0 1 9 3
x
r
1
=
−
b
1
+
b
2
1
−
4
a
1
c
1
2
a
1
equals
=
0.7 7 2 4 7 4 2 1 0 1 9 3
0
.
7
7
2
4
7
4
2
1
0
1
9
3
25
Expression 26: "c" Subscript, "r" 2 , Baseline equals StartFraction, StartRoot, max left parenthesis, "p" Subscript, "a" 2 , Baseline , min left parenthesis, "a" , "p" Subscript, "b" 2 , Baseline , right parenthesis , right parenthesis , EndRoot minus StartRoot, "p" Subscript, "a" 2 , Baseline , EndRoot Over StartNestedFraction, 1 NestedOver StartRoot, max left parenthesis, "p" Subscript, "a" 2 , Baseline , min left parenthesis, "a" , "p" Subscript, "b" 2 , Baseline , right parenthesis , right parenthesis , EndRoot , EndNestedFraction minus StartNestedFraction, 1 NestedOver StartRoot, "p" Subscript, "b" 2 , Baseline , EndRoot , EndNestedFraction , EndFraction equals 1.1 5 5 1 9 4 1 4 1 5 8
c
r
2
=
m
a
x
p
a
2
,
m
i
n
a
,
p
b
2
−
p
a
2
1
m
a
x
p
a
2
,
m
i
n
a
,
p
b
2
−
1
p
b
2
equals
=
1.1 5 5 1 9 4 1 4 1 5 8
1
.
1
5
5
1
9
4
1
4
1
5
8
26
Expression 27: "a" Subscript, 2 , Baseline equals "c" Subscript, "r" 2 , Baseline equals 1.1 5 5 1 9 4 1 4 1 5 8
a
2
=
c
r
2
equals
=
1.1 5 5 1 9 4 1 4 1 5 8
1
.
1
5
5
1
9
4
1
4
1
5
8
27
Expression 28: "b" Subscript, 2 , Baseline equals StartFraction, "L" Subscript, 2 , Baseline "c" Subscript, "r" 2 , Baseline Over StartRoot, "p" Subscript, "b" 2 , Baseline , EndRoot , EndFraction plus "L" Subscript, 2 , Baseline StartRoot, "p" Subscript, "a" 2 , Baseline , EndRoot equals 4.3 1 0 3 8 8 2 8 3 1 6
b
2
=
L
2
c
r
2
p
b
2
+
L
2
p
a
2
equals
=
4.3 1 0 3 8 8 2 8 3 1 6
4
.
3
1
0
3
8
8
2
8
3
1
6
28
Expression 29: "c" Subscript, 2 , Baseline equals negative "L" squared left parenthesis, 1 minus StartFraction, StartRoot, "p" Subscript, "a" 2 , Baseline , EndRoot Over StartRoot, "p" Subscript, "b" 2 , Baseline , EndRoot , EndFraction , right parenthesis equals negative 12
c
2
=
−
L
2
2
1
−
p
a
2
p
b
2
equals
=
negative 12
−
1
2
29
Expression 30: "x" Subscript, "r" 2 , Baseline equals StartFraction, negative "b" Subscript, 2 , Baseline positive StartRoot, "b" squared minus 4 "a" Subscript, 2 , Baseline "c" Subscript, 2 , Baseline , EndRoot Over 2 "a" Subscript, 2 , Baseline , EndFraction equals 1.8 5 8 3 9 2 7 3 8 3 4
x
r
2
=
−
b
2
+
b
2
2
−
4
a
2
c
2
2
a
2
equals
=
1.8 5 8 3 9 2 7 3 8 3 4
1
.
8
5
8
3
9
2
7
3
8
3
4
30
r1: left brace, "a" less than or equal to "p" Subscript, "a" 1 , Baseline : left parenthesis, StartFraction, "L" Subscript, 1 , Baseline Over StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot , EndFraction minus StartFraction, "L" Subscript, 1 , Baseline Over StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot , EndFraction , 0 , right parenthesis , "p" Subscript, "a" 1 , Baseline less than "a" less than "p" Subscript, "b" 1 , Baseline : left parenthesis, "x" Subscript, "r" 1 , Baseline , "c" Subscript, "r" 1 , Baseline "x" Subscript, "r" 1 , Baseline , right parenthesis , left parenthesis, 0 , "L" Subscript, 1 , Baseline StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot minus "L" Subscript, 1 , Baseline StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot , right parenthesis , right brace equals left parenthesis, 0.7 7 2 4 7 4 2 1 0 1 9 3 , 0.9 8 8 7 8 2 9 5 9 5 , right parenthesis Has graph. To audio trace, press ALT+T.
a
≤
p
a
1
:
L
1
p
a
1
−
L
1
p
b
1
,
0
,
p
a
1
<
a
<
p
b
1
:
x
r
1
,
c
r
1
x
r
1
,
0
,
L
1
p
b
1
−
L
1
p
a
1
Label:
equals
=
left parenthesis, 0.7 7 2 4 7 4 2 1 , 0.9 8 8 7 8 2 9 6 , right parenthesis
0
.
7
7
2
4
7
4
2
1
,
0
.
9
8
8
7
8
2
9
6
31
r2: left brace, "a" less than or equal to "p" Subscript, "a" 2 , Baseline : left parenthesis, StartFraction, "L" Subscript, 2 , Baseline Over StartRoot, "p" Subscript, "a" 2 , Baseline , EndRoot , EndFraction minus StartFraction, "L" Subscript, 2 , Baseline Over StartRoot, "p" Subscript, "b" 2 , Baseline , EndRoot , EndFraction , 0 , right parenthesis , "p" Subscript, "a" 2 , Baseline less than "a" less than "p" Subscript, "b" 2 , Baseline : left parenthesis, "x" Subscript, "r" 2 , Baseline , "c" Subscript, "r" 2 , Baseline "x" Subscript, "r" 2 , Baseline , right parenthesis , left parenthesis, 0 , "L" Subscript, 2 , Baseline StartRoot, "p" Subscript, "b" 2 , Baseline , EndRoot minus "L" Subscript, 2 , Baseline StartRoot, "p" Subscript, "a" 2 , Baseline , EndRoot , right parenthesis , right brace equals left parenthesis, 1.8 5 8 3 9 2 7 3 8 3 4 , 2.1 4 6 8 0 4 4 0 4 0 8 , right parenthesis Has graph. To audio trace, press ALT+T.
a
≤
p
a
2
:
L
2
p
a
2
−
L
2
p
b
2
,
0
,
p
a
2
<
a
<
p
b
2
:
x
r
2
,
c
r
2
x
r
2
,
0
,
L
2
p
b
2
−
L
2
p
a
2
Label:
equals
=
left parenthesis, 1.8 5 8 3 9 2 7 4 , 2.1 4 6 8 0 4 4 , right parenthesis
1
.
8
5
8
3
9
2
7
4
,
2
.
1
4
6
8
0
4
4
32
pa1: left parenthesis, StartFraction, "L" Subscript, 2 , Baseline Over StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot , EndFraction , "L" Subscript, 2 , Baseline StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot , right parenthesis equals left parenthesis, 5.6 5 6 8 5 4 2 4 9 4 9 , 2.8 2 8 4 2 7 1 2 4 7 5 , right parenthesis Has graph. To audio trace, press ALT+T.
L
2
p
a
1
,
L
2
p
a
1
Label:
equals
=
left parenthesis, 5.6 5 6 8 5 4 2 5 , 2.8 2 8 4 2 7 1 2 , right parenthesis
5
.
6
5
6
8
5
4
2
5
,
2
.
8
2
8
4
2
7
1
2
33
pa1: left parenthesis, StartFraction, "L" Subscript, 3 , Baseline Over StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot , EndFraction , "L" Subscript, 3 , Baseline StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot , right parenthesis equals left parenthesis, 9.8 9 9 4 9 4 9 3 6 6 1 , 4.9 4 9 7 4 7 4 6 8 3 1 , right parenthesis Has graph. To audio trace, press ALT+T.
L
3
p
a
1
,
L
3
p
a
1
Label:
equals
=
left parenthesis, 9.8 9 9 4 9 4 9 4 , 4.9 4 9 7 4 7 4 7 , right parenthesis
9
.
8
9
9
4
9
4
9
4
,
4
.
9
4
9
7
4
7
4
7
34
pb1: left parenthesis, StartFraction, "L" Subscript, 2 , Baseline Over StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot , EndFraction , "L" Subscript, 2 , Baseline StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot , right parenthesis equals left parenthesis, 2.8 2 8 4 2 7 1 2 4 7 5 , 5.6 5 6 8 5 4 2 4 9 4 9 , right parenthesis Has graph. To audio trace, press ALT+T.
L
2
p
b
1
,
L
2
p
b
1
Label:
equals
=
left parenthesis, 2.8 2 8 4 2 7 1 2 , 5.6 5 6 8 5 4 2 5 , right parenthesis
2
.
8
2
8
4
2
7
1
2
,
5
.
6
5
6
8
5
4
2
5
35
pb1: left parenthesis, StartFraction, "L" Subscript, 3 , Baseline Over StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot , EndFraction , "L" Subscript, 3 , Baseline StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot , right parenthesis
L
3
p
b
1
,
L
3
p
b
1
Label:
equals
=
left parenthesis, 4.9 4 9 7 4 7 4 7 , 9.8 9 9 4 9 4 9 4 , right parenthesis
4
.
9
4
9
7
4
7
4
7
,
9
.
8
9
9
4
9
4
9
4
36
pb2: left parenthesis, StartFraction, "L" Subscript, 2 , Baseline Over StartRoot, "p" Subscript, "b" 2 , Baseline , EndRoot , EndFraction , "L" Subscript, 2 , Baseline StartRoot, "p" Subscript, "b" 2 , Baseline , EndRoot , right parenthesis
L
2
p
b
2
,
L
2
p
b
2
Label:
equals
=
left parenthesis, 2 , 8 , right parenthesis
2
,
8
37
pa2: left parenthesis, StartFraction, "L" Subscript, 2 , Baseline Over StartRoot, "p" Subscript, "a" 2 , Baseline , EndRoot , EndFraction , "L" Subscript, 2 , Baseline StartRoot, "p" Subscript, "a" 2 , Baseline , EndRoot , right parenthesis
L
2
p
a
2
,
L
2
p
a
2
Label:
equals
=
left parenthesis, 8 , 2 , right parenthesis
8
,
2
38
Hidden pa1: left parenthesis, StartFraction, "L" Subscript, 1 , Baseline Over StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot , EndFraction , "L" Subscript, 1 , Baseline StartRoot, "p" Subscript, "a" 1 , Baseline , EndRoot , right parenthesis
L
1
p
a
1
,
L
1
p
a
1
Label:
equals
=
left parenthesis, 4.2 4 2 6 4 0 6 9 , 2.1 2 1 3 2 0 3 4 , right parenthesis
4
.
2
4
2
6
4
0
6
9
,
2
.
1
2
1
3
2
0
3
4
39
Hidden pb1: left parenthesis, StartFraction, "L" Subscript, 1 , Baseline Over StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot , EndFraction , "L" Subscript, 1 , Baseline StartRoot, "p" Subscript, "b" 1 , Baseline , EndRoot , right parenthesis
L
1
p
b
1
,
L
1
p
b
1
Label:
equals
=
left parenthesis, 2.1 2 1 3 2 0 3 4 , 4.2 4 2 6 4 0 6 9 , right parenthesis
2
.
1
2
1
3
2
0
3
4
,
4
.
2
4
2
6
4
0
6
9
40
Expression 41: "h" equals 12.9 5
h
=
1
2
.
9
5
0
0
20
2
0
41
L1: left parenthesis, StartFraction, "L" squared Over "h" , EndFraction , "h" , right parenthesis
L
2
1
h
,
h
Label:
equals
=
left parenthesis, 0.6 9 4 9 8 0 6 9 , 12.9 5 , right parenthesis
0
.
6
9
4
9
8
0
6
9
,
1
2
.
9
5
42
L2: left parenthesis, StartFraction, "L" squared Over "h" , EndFraction , "h" , right parenthesis
L
2
2
h
,
h
Label:
equals
=
left parenthesis, 1.2 3 5 5 2 1 2 4 , 12.9 5 , right parenthesis
1
.
2
3
5
5
2
1
2
4
,
1
2
.
9
5
43
L1 + L2: left parenthesis, StartFraction, "L" squared Over "h" , EndFraction , "h" , right parenthesis
L
2
3
h
,
h
Label:
equals
=
left parenthesis, 3.7 8 3 7 8 3 7 8 , 12.9 5 , right parenthesis
3
.
7
8
3
7
8
3
7
8
,
1
2
.
9
5
44
Expression 45:
45
46
powered by
powered by
p
r1
r2
pa1
pa1
pb1
pb1
pb2
pa2
L1
L2
L1 + L2
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
Log In
or
Sign Up
to save your graphs!
New Blank Graph
Examples
Lines: Slope Intercept Form
example
Lines: Point Slope Form
example
Lines: Two Point Form
example
Parabolas: Standard Form
example
Parabolas: Vertex Form
example
Parabolas: Standard Form + Tangent
example
Trigonometry: Period and Amplitude
example
Trigonometry: Phase
example
Trigonometry: Wave Interference
example
Trigonometry: Unit Circle
example
Conic Sections: Circle
example
Conic Sections: Parabola and Focus
example
Conic Sections: Ellipse with Foci
example
Conic Sections: Hyperbola
example
Polar: Rose
example
Polar: Logarithmic Spiral
example
Polar: Limacon
example
Polar: Conic Sections
example
Parametric: Introduction
example
Parametric: Cycloid
example
Transformations: Translating a Function
example
Transformations: Scaling a Function
example
Transformations: Inverse of a Function
example
Statistics: Linear Regression
example
Statistics: Anscombe's Quartet
example
Statistics: 4th Order Polynomial
example
Lists: Family of sin Curves
example
Lists: Curve Stitching
example
Lists: Plotting a List of Points
example
Calculus: Derivatives
example
Calculus: Secant Line
example
Calculus: Tangent Line
example
Calculus: Taylor Expansion of sin(x)
example
Calculus: Integrals
example
Calculus: Integral with adjustable bounds
example
Calculus: Fundamental Theorem of Calculus
example
Terms of Service
|
Privacy Policy
