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Educational Level

Secondary school, High school and College 
Program Purpose

Provide step by step solutions of your problems using online calculators (online solvers)

Problem Source

Your textbook, etc 
0.
Geometry examples

1. Coordinate Geometry
2. Graphs
1. Graphs  Plotting of mathematical functions f(x) or f(y)
2. Graph  Using Points and Slope
2.1 Points : (3,5),(5,3)
2.2 Points on Xaxis : 3,5,12,7,0
2.3 Points on Yaxis : 3,5,12,7,0
2.4 Lines : x=3y+5; 2x+y=1; x+2y<=5; x+y>=15
2.5 Line using Slope & point : Slope=7 and Point=(4,6)
2.6 Line using Slope & YIntercept : Slope=2 and YIntercept=4
2.7 Line passing through two points : Point1=(3,5) and Point2=(5,3)
3. Circle
4. Ellipse
5. Parabola
6. Hyperbola
7. Polar Graph
3. Area
1. Circle
2. SemiCircle
3. RegularHexagon
4. Square
5. Rectangle
6. Parallelogram
7. Rhombus
8. Trapezium
9. Scalene Triangle
10. Right angle Triangle
11. Equilateral Triangle
12. Isosceles Triangle
13. Sector Segment
4. Volume
1. Cuboid
2. Cube
3. Cylinder
4. Cone
5. Sphere
6. HemiSphere
5. Pythagorean Theorem

1.
General Graph

1. `y = x`
2. `y <= sin(x)`
3. `y >= cos(x)`
4. `y = sqrt(x)`
5. `y <= sqrt(x^33x)`
6. `y >= x`
7. `y = x^3x`
8. `y <= (e^xe^(x))/2`
1. `x = sin(y)`
2. `x <= cos(y)`
3. `x >= sqrt(y)`
4. `x = sqrt(y^33y)`
5. `x <= y`
6. `x >= sin(y)^3+cos(y)^3`
7. `x = y+sin(y)`
8. `x <= (sin(9y)+sin(10y))*sin(0.1y)`


2.
Graph  Using Points and Slope

1. Points like (3,5),(5,3)
2. Points on Xaxis like 3,5,12,7,0
3. Points on Yaxis like 3,5,12,7,0
4. Lines like x=3y+5; 2x+y=1; x+2y<=5; x+y>=15
5. Line using Slope & point like Slope=7 and Point=(4,6)
6. Line using Slope & YIntercept like Slope=2 and YIntercept=4
7. Line passing through two points like Point1=(3,5) and Point2=(5,3)



3.
Circle

1. Circle1
`X^2 + Y^2 = 9`
2. Circle2
`(X+1)^2 + Y^2 = 12`
3. Circle3
`X^2 + (Y2)^2 = 15`
4. Circle4
`(X+1)^2 + (Y2)^2 = 9`


4.
Ellipse

1. Ellipse1
`X^2/4 + Y^2/9 = 9`
2. Ellipse2
`(X+1)^2/4 + Y^2/9 = 12`
3. Ellipse3
`X^2/4 + (Y2)^2/9 = 15`
4. Ellipse4
`(X+1)^2/4 + (Y2)^2/9 = 9`



5.
Parabola

1. Parabola1
`Y = 3X^2`
2. Parabola2
`Y = 3X^2 + 1`
3. Parabola3
`Y = 3(X+1)^2`
4. Parabola4
`Y = 3(X+1)^2 + 1`
5. Parabola5
`X = 3Y^2`
6. Parabola6
`X = 3Y^2 + 1`
7. Parabola7
`X = 3(Y+1)^2`
8. Parabola8
`X = 3(Y+1)^2 + 1`


6.
Hyperbola

1. Hyperbola1
`X^2/4  Y^2/9 = 9`
2. Hyperbola2
`2. (X+1)^2/4  Y^2/9 = 12`
3. Hyperbola3
`X^2/4  (Y2)^2/9 = 15`
4. Hyperbola4
`(X+1)^2/4  (Y2)^2/9 = 9`
5. Hyperbola5
`Y^2/4  X^2/9 = 9`
6. Hyperbola6
`(Y+1)^2/4  X^2/9 = 12`
7. Hyperbola7
`Y^2/4  (X2)^2/9 = 15`
8. Hyperbola8
`(Y+1)^2/4  (X2)^2/9 = 9`



7.
Polar Graph

1. `R = 4*cos(2*t)`
2. `R = 4*sin(2*t)`
3. `R = 24*sin(2*t)`
4. `R = 24*cos(2*t)`
5. `R = 2+4*cos(2*t)`
6. `R = 2+4*sin(2*t)`















7.
Rhombus

Radius `(r_1) = (d_1)/2`
Radius `(r_2) = (d_2)/2`
Side `(a) = sqrt(r_1^2 + r_2^2)`
Perimeter `(P) = 4 a`
Area `(SA) = (d_1 d_2)/2`
I know that for a rhombus d1 = 10 and d2 = 24 . From this find out Area of the rhombus.
`"Here, we have " d_1 = 10" and " d_2 = 24" (Given)"`
`a^2 = (d_1/2)^2 + (d_2/2)^2`
`a^2 = (10/2)^2 + (24/2)^2`
`a^2 = (5)^2 + (12)^2`
`a^2 = 169`
`a = 13`
`"Perimeter" = 4 * a`
` = 4 * 13`
` = 52`
`"Area" = 1/2 " (Product of diagonals)"`
` = 1/2 * d_1 * d_2`
` = 1/2 * 10 * 24`
` = 120`












1.
Cuboid

Diagonal `(d) = sqrt(l^2+ b^2+ h^2)`
Surface Area `(SA) = 2 (lb + bh + hl)`
Volume `(V) = lbh`
I know that for a cuboid Length = 3 , Breadth = 4 , and Height = 5 . From this find out Volume of the cuboid.
`"Here, we have " l = 3, b=4, h=5" (Given)"`
`"Diagonal"^2 = l^2 + b^2 + h^2`
`"Diagonal"^2 = 3^2 + 4^2 + 5^2`
`"Diagonal"^2 = 50`
`Diagonal = 7.0711`
`"Here, we have " l = 3, b=4, h=5" (Given)"`
`"Volume" = l * b * h`
` = 3 * 4 * 5`
` = 60`
`"Here, we have " l = 3, b=4, h=5" (Given)"`
`"Total Surface Area" = 2 (lb + bh + lh)`
` = 2 * (3 * 4 + 4 * 5 + 3 * 5)`
` = 2 * (47)`
` = 94`
`"Here, we have " l = 3, b=4, h=5" (Given)"`
`"Curved Surface Area" = 2h (l + b)`
` = 2 * 5 (3 + 4)`
` = 70`


2.
Cube

diameter `(d) = sqrt(2) l`
Diagonal `= sqrt(3) l`
Surface Area `(SA) = 6 l^2`
Volume `(V) = l^3`
I know that for a cube Length = 3 . From this find out Volume of the cube.
`"Here, we have " l = 3`
`"Diagonal" = sqrt(3) l`
` = sqrt(3) * 3`
` = 5.1962`
`"Here, we have " l = 3`
`"Volume" = l^3`
` = 3^3`
` = 27`
`"Here, we have " l = 3`
`"Total Surface Area" = 6 l^2`
` = 6 * 3^2`
` = 6 * 9`
` = 54`
`"Here, we have " l = 3`
`"Curved Surface Area" = 4 l^2`
` = 4 * 3^2`
` = 4 * 9`
` = 36`




4.
Cone

Height `(h) = sqrt(l^2  r^2)`
Curved Surface Area `(CSA) = pi r l`
Total Surface Area `(TSA) = pi r (l + r)`
Volume `(V) = (pi r^2 h)/3`
I know that for a cone Radius = 3 and Length = 5 . From this find out Volume of the cone.
`"Here, we have Radius "(r) = 3" and Slant Height " (l) = 5" (Given)"`
`l^2 = r^2 + h^2`
`h^2 = l^2  r^2`
`h^2 = 5^2  3^2`
`h^2 = 16`
`h = 4`
`"Volume" = (pi r^2 h)/3`
` = (pi * 3^2 * 4)/3`
` = 37.6991`
`"Total Surface Area" = pi r (l + r)`
` = pi * 3 (5 + 3)`
` = 75.3982`
`"Curved Surface Area" = pi r l`
` = pi * 3 * 5`
` = 47.1239`






Pythagorean Theorem
: In a right angled triangle, the square of the length of the hypotenuse
is equal to the sum of the squares of the lengths of the remaining sides.
i.e. `AC^2 = AB^2 + BC^2`
Using Pythagoras
Theorem, Find out AC when AB = 5 and BC = 12
Here AB=5 and BC=12 (Given)
We know that,
In triangle ABC, by Pythagoras' theorem
`AC^2 = AB^2 + BC^2`
`AC^2 = 5^2 + 12^2`
`AC^2 = 25 + 144`
`AC^2 = 169`
`AC = 13`







