Wednesday, April 17, 2013

Quadratic equation solver (High School)


(2x-15)(2x-7)-(x-36)(x-8)+36=0
4x²-14x-30x+105-(x²-8x-36x+288)+36=0
4x²-14x-30x+105-x²+8x+36-288+36=0
3x²-147=0
3x²=147
x²=147/3
x=√49
x1=+7    x2=-7

Division of complex numbers



i2 = −1

3-5 i/7+2 i=3-5 i/7+2 i*7-2 i/7-2 i=21-6 i-35 i+10 i²/7²+2²=21-10-41 i²/49+4=
=11-41 i/53=11/53-41/53 i

Arithmetic root



Example 1.

(2√5+√19)(2√5-√19)=(2√5)²-( √19)²=4*5-19=20-19=1




Example 2.
(3√6-2√16)(2√16+3√6)=(3√6-2√16)(3√6+2√16)=(3√6)²-(2√16)²=
=9*6-4*16=54-64=-10

Surface area and volume of regular four-sided pyramid




Calculate the surface area and volume of regular four-sided pyramid if B = 36cm² and height 4 cm.

Solved:


B=36cm²        H=4cm                  M=4*a*h/2              P=M+B
B=√36            h²=H²+(a/2)²         M=4*6*5/2              P=60+36
B=6cm            h²=4²+(6/2)²         M=60cm²                 P=96cm²
a=6cm             h²=16+9
                        h=√25                  
                        h=5cm                  V=B*H/3
                                                     V=36*4/3
                                                     V=48cm²

Proper quadrilateral prism (primary school)

Calculate the surface proper quadrilateral prism if the base edges 4cm and 8cm high.

Solved:


a=6cm                 M=3a*H           P=2B+M
H=8cm                M=3*6*8          P=2*9√3+144
B=a²√3/4             M=18*8            P=18√3+144 cm²
B=6²√3/4             M=144cm²
B=36√3/4
B=9√3

Cube surface (primary school)

The sum of the length of the edge of a cube is 48cm. Calculate the surface.

Solved:


O=48cm          P=6a²                  
O=12a             P=6*4²
48=12a            P=6*16
a=48:12           P=96cm²
a=4cm

Surfaces of the cube (primary school)

Calculate the surface of a cube if the diagonal 3√2


Solved:


d=a√2                             P=6a²                  
3√2=a√2                         P=6*3²
a=3cm                             P=6*9
                                        P=54cm²