Why Do We Use lP+mQ+nR=0 in the Solution of dx/P=dy/Q=dz/R?

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In summary, "Dx/P = dy/Q = dz/R" is a formula used to represent the relationship between three variables and their corresponding coefficients. It can be solved for one variable using algebraic manipulation and has various real-world applications in fields such as physics, economics, and chemistry. Additionally, the formula can be modified by changing the values of the coefficients to fit different scenarios.
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abrowaqas
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Dx/P = dy/Q = dz/R why we take lP+mQ+nR=0 and then solve?

why we take lP+mQ+nR = 0 in solution of dx/P=dy/Q=dz/R i-e ldx+mdy+ndz/(lP+mQ+nR) .. when lP+mQ+nR = 0 the expression goes to infinity .. how then we take integral of ldx+mdy+ndz as lx+my+nz= C. kindly clear
 
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Let the constant function be dk=dx/P = dy/Q = dz/R. Then we have
ldx+mdy+ndz= (lP+mQ+nR)dk = 0. Hence the solution.
 

FAQ: Why Do We Use lP+mQ+nR=0 in the Solution of dx/P=dy/Q=dz/R?

What does "Dx/P = dy/Q = dz/R" mean?

"Dx/P = dy/Q = dz/R" is a formula that represents the relationship between three variables: Dx, dy, and dz. The letters P, Q, and R represent constants or coefficients that are used to scale the variables. This formula is often used in physics and mathematics to represent rates of change or proportions.

How do you solve for one variable in "Dx/P = dy/Q = dz/R"?

To solve for one variable, you can use algebraic manipulation to isolate the variable on one side of the equation. For example, if you want to solve for Dx, you can multiply both sides of the equation by P, and then divide by Q and R to get Dx = (P/Q)dy = (P/R)dz.

Can "Dx/P = dy/Q = dz/R" be used in all types of equations?

No, this formula is specifically used for representing relationships between three variables. It may not be applicable to all types of equations, such as those with more or less than three variables.

What are some real-world applications of "Dx/P = dy/Q = dz/R"?

This formula has many real-world applications, such as in physics for calculating velocity, acceleration, and other rates of change. It is also used in economics to represent supply and demand relationships, and in chemistry to calculate reaction rates.

How can "Dx/P = dy/Q = dz/R" be modified for different situations?

The constants or coefficients (P, Q, and R) can be changed to fit different situations and represent different scales or proportions. For example, in physics, the constant P may represent time, while in economics, the constant Q may represent price. By changing these values, the formula can be applied to different scenarios and yield different results.

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