IQ Math-شغل مخك

Selected solved problems:-

15m+8n=1000
Soluation;
m=8k, n=125-15k

For k=0, to 8
No of ways=9

Selected solved problems:-

(R√3-R-r)²=r²+(R-2√3)²,
(R/2)²+((√3/2)R-(R√3-R-r))²=12+r²

r = 2(√3-1), R = 6

Painted area= (3*6√3/2)-π*4(√3-1)²-18((π/3)-√3/2)
=5.593cm²

Square, Semicircle
Find X

Selected, solved problems:

θ=60
β=30

White area= 2A(ABC)+8((π/6)-0.5)-8((π/3)-(√3/2))=8(√3-π/3)

Blue area= 16-8(√3-π/3)
≈10.52cm²

Selected, solved problems:
(a-2)²+(b-2)²=4,
(b-1)²+1=(a-1)²+1-4

a≈3.77438, b≈2.92281
Area=√(b²+1)=3.0891u²

Selected, solved problems:
x√2=10-2z,
z(10-z)=2x²

x = √10, z = 5-√5
Area=2x*x=20cm²

Selected, solved problems:

R/z=2R/(z+12),
R/13=2R/(x+13),
z²+R²=13²,
4R²+(z+12)²=(x+13)²
A(NAB)=R(z+12)

R = 5, x = 13, z = 12
A = 120cm²

A=0.487(2.17+1.854)/2 =0.98

B=1.09*1/2=0.545

A/B=0.98/0.545≈1.8

Solved SELECTED problems:

x²+y²=100,
(x-10)²+y²=49
y= √(49-(x-10)²)
p: x=151/20
(x-5)²+y²=25
y= √(25-(x-5)²)
Red= (25π/4)-(49/4)((π/2)-1)=(98+π)/8

Blue area=
∫ √(49-(x-10)²)-√(25-(x-5)²)dx[5,p] =2.77318
+
∫ √(100-x²)-√(25-(x-5)²)dx[p,10] =3.54197
Red=3.54197+2.77318=
6.31515

Ratio=B/R= 6.31515/((98+π)/8)=1/2

Solved SELECTED problems:

(p+5)²=4r²+7²
(x-5)²+(y-r)²=r²
x²+y²=(p+5)²

(5)²+(y-r)²=r²
25+y²-2yr=0
y =√(25-r²)+r, r-√(25-r²)

25=r²-(25-r²)
r=5
x=p=√149-5=7.21

Solved SELECTED problems:
xp=54,
(y-p)(x-z)=24,
yz=30

xy=90
s=90-54=36u²

Solved SELECTED problems:
r=1/(2√3)
y=0.5-r
x=√(1+(0.5-1/(2√3))²)
=1.0221u