How to find intersection point of two lines

Topic:-Intersection Point

a point where lines intersect

point - a geometric element that has position but no extension; "a point is defined by its coordinates"

Let's see how to find this intersection point of two lines

Question:-

Find the intersection point of two lines

3x+2y=5 and x+4y=0


Answer:-

Let's say


3x+2y=5 ---------> 1

x+4y=0 ---------->2


Take the equation 2

x+4y=0

x= -4y----->3

Substitute this in equation 1

We get

3(-4y)+2y=5

-12y+2y=5

-10y=5

y= 5/-10

y= - ½

Substitute this in 3

x= -4(-½)

x= 2

So ,The intersection point is

(2,-½)


For more help on this ,you can reply me.

a problem on inequality

Topic:-Inequality
What is inequality is defined along with a example in this math help
An inequality is a statement about the relative size or order of two objects, or about whether they are the same or not (See also: equality). Inequality rules are

• The notation a < b means that a is less than b.
• The notation a > b means that a is greater than b.
• The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.

In each statement above, a is not equal to b. These relations are known as strict inequalities. The notation a < b may also be read as "a is strictly less than b".

Question:-

Solve the following inequality

y-7 > -12


Answer:-
 y-7 > -12

add 7 on both sides

y-7+7 > -12+7

 y > -5

So y є (-5,∞) is the Answer  

For more help on this ,Please reply me.

problem on Angular speed

Topic :- Angular speed of EarthThe Earth turns toward the east, we see the sky
turning toward the west at this same rate.Then how to find angular speed for it.Let's look at it.

Question:"Find the angular speed of the Earth's rotation on it's axis",
Answer:-

The earth rotate once about it's axis in 24 hours

That is 2π radians in 24 hours.

Therefore angular speed =


      2π
    ------  rad/hour
      24

    Lets see how to convert in seconds


       2π
  =  ----------
      24*60*60

  = 7.272*10-5rad/sec

So the angular speed of earth is7.272*10-5rad/sec
.

For similar kind of help ,you can reply me.

A Problem on Volume of a Cube/Geometrical Figure Cube

All the geometrical construction and geometrical figures like cube, cuboid, prism etc come under construction math and construction geometry where you will get more information about these geometrical figures and there attributes.

Topic : Volume of a cube

A Cube is a Geometrical Figure with dimension of equal sides, here is one such example on Cube, to Find length of the side of cube, given volume of cube using indice laws.

Question : The volume of a cube is given by V = s³, where s is the length of a side. Find the length of a side of a cube if the volume is 700 in³.Round the answer to three decimal places.

Solution :

Given V = 700 in³

Also, volume of a cube is given by

V = s³

=> 700 = s³

=> s³ = 700

=> s = cuberoot(700)

=> s = 8.697

Length of a side of cube = 8.697 inches.

Word problem on Function and gas concentration as its dependencies

Functions are denoted as shown in the figure where there will be dependencies of one variable value to another.

Topic : Functions and variables values.

Variables, co-efficient are the terms found in functions.

Problem : The table lists future concentrations of a certain green house gas in parts per billion (ppb), If current trends continue.

a) Let x = 0 correspond to 2010 and x = 20 correspond to 2030. Find C and a so that f(x) = Ca^x models the data.

b) Estimate the gas concentration in 2021.

Year ------ Gas(ppb)
2010 ------ 0.74 (when x = 0)
2015 ------ 0.86
2020 ------ 0.99
2025 ------ 1.15
2030 ------ 1.34 (when x = 20)

Solution :

a) We have function ,
f(x) = Ca^x

x = 0 ; f(0) = Ca⁰ = C*1 = C

So f(0) = 0.74 ; C = 0.74

and x = 20 ; f(x) = C a²⁰ = 0.74 a²⁰

f(20) = 1.34 (from the table)

So 1.34 = 0.74 a²⁰ ; a²⁰ = 1.34/0.74 = 1.8108

So a = 1.0301


b) To find gas concentration at the year 2021, we have to find f(21)

f(21) = Ca²¹ = 0.74 (1.0301)²¹

= 0.74 * 1.8641

= 1.37943

So f(21) approximately 1.38

Therefore gas concentration at 2021 will be 1.38

-->

If you have any queries related to this problem please do write to us and our algebra help will be happy respond.

Question on Integrating Factor Method for Solving Differential Equation

Topic : Integrating Factor

Question : Explain Integrating Factor Method for Solving Differential Equation

Solution :
Suppose we have this equation to solve:
dy + y = x
dx
In this case we cannot separate the variables and introducing a new variable doesn't help either. So we need to use an entirely different method, known as Integrating Factor Method.
Here's the typical equation for which we can use this method:
dy + yP(x) = Q(x)
dx
Here the functions P(x) and Q(x) can be any functions of x, in the example above they were 1 and x respectively.
Step One: calculate the integral of the function P(x).
Step Two: the integrating factor, which we'll call IF, is defined as the exponential of this, i.e. it's defined by :
Integrating Factor = IF = e^(∫P(x) dx)
Step Three: the solution to the equation is given by:
y(x) = 1/IF ∫Q(x) IF dx
Now let us understand this using an example-
dy + y = x
dx
So P(x)=1 and Q(x)=x. The integrating factor is therefore ex, since the integral of 1 is x. (No need for a constant of integration, that's because if you do put one in it will cancel out later on anyway)
So, we can write down the solution y(x) of the equation using the "mysterious" formula given in Step Three:
y(x) = 1/IF ∫Q(x) IF dx
In this case that's:
y(x) = 1/e^x ∫xe^x dx
We can do that integral using integration by part. The result is:
y(x) = e^(-x) (xe^x - e^x + c)
which implies to
y(x) = x - 1 + ce^(-x)

Problem to Solve Simultaneous Equations by Substitution Method

Topic : Substitution Method

Problem : Solve using Substitution Method.

y - 2x = - 6

2y - x = 5

Solution :