a/sinA=b/sinB=c/sinC=2R
note:
In ...
rare
Represents the radius of the circumscribed circle of a triangle.
cosine theorem
b^2=a^2+c^2-2accosB
Note: Angle B is the included angle between side A and side C..
the standard equation of the circle
(x-a)^2+(y-b)^2=^r2
Note: (a, b) is the central coordinate.
Circular general equation
x^2+y^2+Dx+Ey+F=0
Note: d 2+e 2-4f > 0
Parabolic standard equation
y^2=2px
y^2=-2px
x^2=2py
x^2=-2py
Transverse area of right prism
S=c*h
Oblique prism side area
S=c'*h
Side area of regular pyramid
S= 1/2c*h '
Transverse area of regular prism
S= 1/2(c+c')h '
Yuantai lateral area
s = 1/2(c+c’)l = pi(R+R)l
Surface area of ball
S=4pi*r2
Cylindrical side area
S=c*h=2pi*h
Cone lateral area
S= 1/2*c*l=pi*r*l
Arc length formula
l=a*r
A is the radian number r of the central angle
& gt0
Sector area formula
s= 1/2*l*r
Cone volume formula
V= 1/3*S*H
Cone volume formula
V= 1/3*pi*r2h
Oblique prism volume
V=S'L
Note: where s' is the area of the straight line,
L is the length of the side.
Cylinder volume formula
V=s*h
cylinder
V=pi*r2h
The key to the problem of "cattle eating grass";
1. The original amount of grass on the grassland
2. The number of grass growing on the grassland every day.
3. The amount of grass cattle eat every day
A+B* days = number of cattle * number of days to eat *C
Primary school olympiad formula
Formula of sum and difference problem
(sum+difference) ÷ 2 = large number
(sum and difference) ÷ 2 = decimal
Summation formula and multiple problems
Sum \ (multiple-1) = decimal
Decimal × multiple = large number
(or
And-decimal = large number)
Formula of differential multiple problems
Difference ÷ (multiple-1) = decimal
Decimal × multiple = large number
(or
Decimal+difference = large number)
Tree planting formula
1
The problem of planting trees on non-closed lines can be divided into the following three situations:
(1) If trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes+1 = total length-1.
Total length = plant spacing × (number of plants-1)
Plant spacing = total length ÷ (number of plants-1)
2 If you want to plant trees at one end of the unclosed line and not at the other end, then:
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
Formula of profit and loss problem
(Profit+Loss) ÷ Difference between two distributions = number of shares participating in distribution.
(Big profit-small profit) ÷ Difference between two distributions = number of shares participating in distribution.
(big loss-small loss) ÷ The difference between two distributions = the number of shares participating in the distribution.
The formula of encounter problem
Meeting distance = speed × meeting time
Meeting time = meeting distance/speed and
Speed Sum = Meeting Distance/Meeting Time
The formula for tracing the problem
Catch-up distance = speed difference× catch-up time
Catch-up time = catch-up distance ÷ speed difference
Speed difference = catching distance ÷ catching time
Tap water problem
Downstream velocity = still water velocity+current velocity
Countercurrent velocity = still water velocity-current velocity
Still water velocity = (downstream velocity+countercurrent velocity) ÷2
Water velocity = (downstream velocity-countercurrent velocity) ÷2
Formula of concentration problem
Solute weight+solvent weight = solution weight.
The weight of solute/solution × 100% = concentration.
Solution weight × concentration = solute weight
Solute weight-concentration = solution weight.
Profit formula and discount problem
Profit = selling price-cost
Profit rate = profit/cost × 100% = (selling price/cost-1) × 100%.
Up and down amount = principal × up and down percentage
Discount = actual selling price ÷ original selling price× 1 00% (discount <1)
Interest = principal × interest rate× time
After-tax interest = principal × interest rate × time × (1-20%)
(Note: 1.00 interest tax was cancelled by+00 in June 2008; 2. The tax rate depends on the topic, not necessarily 20%, but if the topic has no relevant content, it is generally 20% by default. )