Question to Find the Slope of given Straight line Equation

Here is a Linear Programming problem on Slope and y intercept of a Straight line, Straight line equation is a linear equation in two variables.
Slope is a the ratio of the altitude change to the horizontal distance between any two points on the line.
y-intercept is the y-value of the point where the graph of the function or a relation intercepts the y-axis of the rectangular coordinate system (x = 0)

Topic : Slope and y-intercept of a Straight Line

This the simple and direct question to find slope and y intercept.

Problem : Given straight line is 4x -8y - 32 = 0, find the slope and y-intercept of the straight line.
Solution :
Slope is always denoted by 'm'
and Slope = - Co-efficient of x / Co-efficient of y
So from the given straight line 4x - 8y - 32 = 0
=> - 4/- 8 = 1/2
Slope = 1/2

Now to find y-intercept
put x = 0 in the given straight line linear equation,
So 4x - 8y - 32 = 0
-8y - 32 = 0
=> - y = 32/8
=> y = - 4
=> y-intercept is (0,-4)

You can find lot more problems related to the linear programming problems in geometry help and algebra help.

Word Problem on Equation of Circular Orbit of a Satellite

Satellites revolving around the earth forms a circular orbit, hence below word problem describes how to derive equation of that circular orbit which is same as finding equation of circle.

Topic : Circular Orbit of a Satellite

Circular Orbit is considered from the center of the earth.

Question : Weather Satellites. Earth is represented on a map of a portion of the solar system so that its surface is the circle with equation. A weather satellite circle 0.6unit above earth with the center of its circular orbit at the center of earth. Find the equation of the orbit of the satellite on this map.

Solution :

Equation is x² + y² + 2x + 4y - 4091 = 0

adding and subtracting 1 and 4 ;

x² + 2x + 1 + y² + 4y + 4 = 4091 + 1 + 4

(x+1)² + (y+2)² = 4096

(x+1)² + (y+2)² = 64²

So the earth is represented by (x+1)² + (y+2)² = 64²

given a weather satellite circle 0.6unit above earth with the center of its circular orbit at the center of earth.

So radius of this orbit would be 64.6

Thus the equation of orbit is

(x + 1)² + (y + 2)² = (64.6)² = 4173.16

x² + 2x + 1 + y² + 4y + 4 = 4173.16

x² + y² + 2x + 4y + 4 = 4173.16

x² + y² + 2x + 4y = 4173.16

x² + y² + 2x + 4y = 4168.6

So orbit is represented by the equation x² + y² + 2x + 4y -4168.6 = 0


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Question to List Formulas for Volume of Geometrical Figures

Topic : Volume Formulas

Question : List the Formula for all kind of Geometrical figures.

Solution :

Problem to Find Unknown Values of Angles of Triangles

Topic : Angles of Triangle

Question to Indicate Order of Place Value with with an Example

Topic : Place Value

Question : Indicate Order of Place Value in a Number.

Solution :

A Simple Integration Problem

Topic : Integration

Problem : Integrate x^3 ln x



Solution :

Solved Differential Equation

Topic : Differential Equation

Problem : If y = 4 Sin 3x prove y" + 9y = 0

Solution :
y = 4 Sin 3x
differentiate with respect to x
y' = 4 Cos 3x . 3
y' = 12 Cos 3x
Again differentiate with respect to x
y" = 12 (- Sin 3x . 3)
y" = - 36 Sin 3x

Now consider y" + 9y = 0
Substitute the value of y and y"
-36 Sin 3x + 9(4 Sin 3x)
-36 Sin 3x + 36 Sin 3x = 0
Hence proved