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Formulae of Algebra III
26.12.2012, 0:53:48 AM
Algebra

WordExcel
 ax²+2kx+c=0

D₁=k²−ac

x=(−k±√D͞₁)/a
 ax^2+2kx+c=0

D(1)=k^2-ac

x=(-k(+-)sqrt(D(1)))/a
 △ABC, ∠C=90°, BC=a, AC=b, AB=c, CO=h, AO=b₍, BO=a₍:
b
₍+a₍=c
△AOC△BOC△ABC
b=
√b͞₍͞c
h=√a͞₍͞b͞₍
 triangle(ABC), angle(C)=90*degree(), BC=a, AC=b, AB=c, CO=h, AO=b(c), BO=a(c):
b(c)+a(c)=c
triangle(AOC)=similar(triangle(BOC))=similar(triangle(ABC))
b=sqrt(b(c)c)
h=sqrt(b(c)a(c))
 Aᵏ=n!/(n−k)! A(n;k)=n!/(n-k)!
 Cᵏ=n!/(k!(n−k)!) C(n;k)=n!/(k!(n-k)!)
 H≤G≤x̄ H(<=)G(<=)average(x)
 △ABC, ∠C=90°:
sinA=cosB=BC/AB
cosA=sinB=AC/AB
tgA=ctgB=BC/AC=sinA/cosA=cosB/sinB
ctgA=tgB=AC/BC=cosA/sinA=sinB/cosB
sin²A+cos²A=sin²B+cos²B=1
 triangle(ABC), angle(C)=90*degree():
sin(A)=cos(B)=BC/AB
cos(A)=sin(B)=AC/AB
tg(A)=ctg(B)=BC/AC=sin(A)/cos(A)=cos(A)/sin(B)
ctg(A)=tg(B)=AC/BC=cos(A)/sin(A)=sin(B)/cos(B)
sin(A)^2+cos(A)^2=sin(B)^2+cos(B)^2=1
 CIRCUMFERENCE WITH CENTER O, RADIUS OA AND TANGENT p:
p
⊥OA
 CIRCUMFERENCE WITH CENTER O, RADIUS OA AND TANGENT p:
p=perpend(OA)
 CIRCUMFERENCE WITH CENTER O, RADII OB AND OC, AND TANGENTS AB AND AC:
AB=AC
∠1=∠2
 CIRCUMFERENCE WITH CENTER O, RADII OB AND OC, AND TANGENTS AB AND AC:
AB=AC
angle(1)=angle(2)
 CIRCUMFERENCE WITH CENTER O, RADII OA AND OB, AND ARC ALB:
⌒ALB=∠AOB
 CIRCUMFERENCE WITH CENTER O, RADII OA AND OB, AND ARC ALB:
arc(ALB)=angle(AOB)
 CIRCUMFERENCE WITH CENTER O, CHORDS AB AND BC, AND ARC ALC:
⌒ALC=2×∠ABC
 CIRCUMFERENCE WITH CENTER O, CHORDS AB AND BC, AND ARC ALC:
arc(ALC)=2*angle(ABC)
 CIRCUMFERENCE WITH CENTER O, TANGENT AB, SECANT AN AND CHORD MN:
AB²=AN×AM
 CIRCUMFERENCE WITH CENTER O, TANGENT AB, SECANT AN AND CHORD MN:
AB^2=AN*AM
 CIRCUMFERENCE WITH CENTER O, TANGENT AB, CHORD AC AND ARC ALC:
⌒ALC=2×∠BAC
 CIRCUMFERENCE WITH CENTER O, TANGENT AB, CHORD AC AND ARC ALC:
arc(ALC)=2*angle(BAC)
 a⁻ⁿ=1/aⁿ a^(-n)=1/a^n
 ∠BAC, ∠BAK=∠CAK, KM⊥AB, KN⊥AC:
MK=NK
 angle(BAC), angle(BAK)=angle(CAK), KM=perpend(AB), KN=perpend(AC):
MK=NK
 ABMN, AN=BN:
AC=BC
 AB=perpend(MN), AN=BN:
AC=BC
 △ABC WITH INSCRIBED CIRCUMFERENCE WITH CENTER O AND RADIUS r, p=P/2:
S=pr
 triangle(ABC) WITH INSCRIBED CIRCUMFERENCE WITH CENTER O AND RADIUS r, p=P/2:
S=pr
 △ABC, A̅B⃗=a⃗, B̅C⃗=b⃗:
a⃗+b⃗=A̅B⃗+B̅C=C
 triangle(ABC), vector(AB)=vector(a), vector(BC)=vector(b):
vector(a)+vector(b)=vector(AB)+vector(BC)=vector(AC)
 PARALLELOGRAM ABCD, A̅B⃗=C̅D⃗=a⃗, B̅C⃗=A̅D⃗=b⃗:
a⃗+b⃗=b⃗+a⃗=A̅C⃗
 PARALLELOGRAM ABCD, vector(AB)=vector(CD)=vector(a), vector(BC)=vector(AD)=vector(b):
vector(a)+vector(b)=
vector(b)+vector(a)=vector(AC)
 △ABC, A̅B⃗=a⃗, C⃗=b⃗:
ab⃗=C̅B⃗
 triangle(ABC), vector(AB)=vector(a), vector(AC)=vector(b):
vector(a)-vector(b)=vector(CB)
 S=ab×sinC/2 S=ab*sin(C)/2
 a/sinA=b/sinB=c/sinC a/sin(A)=b/sin(B)=c/sin(C)
 a²=b²+c²−2bc×cosA a^2=b^2+c^2-2bc*cos(A)
 a⃗b=|a⃗||b⃗|cosA=x₁x₂+y₁y vector(a)*vector(b)=|vector(a)|*|vector(b)|*cos(A)=x(1)x(2)+y(1)y(2)
 aₙ=2R×sin(180°/n) a(n)=2R*sin(180*degree()/n)
 r=R×cos(180°/n) r=R*cos(180*degree()/n)
 l=πrα/180 l=pi()*r*alpha()/180
 S=πr²α/360 S=pi()*r^2*alpha()/360
 Sₙ=(2a₁+d(n1))n/2 S(n)=(2a(1)+d(n-1))n/2
 Sₙ=b₁(q−1)/(q1) S(n)=b(1)(q^n-1)/(q-1)

Category: My files | Added by: Elektronika_XQ-19 | Tags: algebra, math
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