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John bikes 22 km per hour and starts at mile 10. Gwyn bikes 28 km per hour and starts at mile 0. Which system of linear equations represents this situation?
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Steps in solving problems involving systems of linear equations?
The answer depends on the level of your knowledge. The High level, simple answer is first. The Low level slog follows:HIGH LEVEL, SIMPLESuppose you have n equations of the forma11x1 + a12x2 + ... + a1nxn = bn wherethe as are coefficients,x1, x2, ... xn are the unknown variablesandb1, b2, ... bn are the constants.Write the n linear equations in n unknowns in the form Ax= bwhereA is an n*n matrix of coefficientsx is the n*1 matrix of the unknown variablesandb is the n*1 matrix of the constants.Find the inverse of A.Then x = A-1b.The above method works if the system has a unique solution. If the n equations are not independent, you will need to use a generalised inverse and that starts to get rather complicated. If they are inconsistent, then neither the inverse nor generalised inverse will be found.LOW LEVEL SLOGUse the first equation to express x1 in terms of the other variables. Substitute this value for x1 in the remaining n-1 equations. You now have n-1 equations in n-1 unknown variables.Use the first of the new equations to express x2 in terms of the other variables. Substitute in remaining equations. You now have n-2 equations in n-2 unknown variables.Continue until you have 1 equation in 1 unknown.That will be of the form pxn = q so that xn = q/p.Substitute this value into one of the equations at the 2-equations-in-2-unknowns stage. That will give you xn-1.Work your way back to the top.The two methods are equivalent. There are shortcuts available for matrix inversion (eg using determinants), but these are too complicated to go into here.
How do you get the formula center of curvature?
This starts with the collocation circle to go through the three points on the curve. First write the equation of a circle. Then write three equations that force the collocation circle to go through the three points on the curve. Last, solve the equations for a, b, and r.
What if linear equations starts with a negative?
Either move the negative over to the other side to become positive, or divide the entire equation by -1 to get it to a positive. Example: -3x + 12 = 30 Move the -3x over to get 12 = 30 + 3x 12 - 30 = 3x - 18 = 3x - 6 = x OR Divide by -1 to get 3x - 12 = - 30 3x = - 30 + 12 3x = -18 x = -6
What geometric shape starts with the letter j?
The geometric shape that starts with the letter J is a "Jacobian." In mathematics, a Jacobian matrix is a matrix of first-order partial derivatives for a vector-valued function. It is used in multivariable calculus and differential equations to study the relationship between different variables in a system.
How to derive the centre of curvature?
This involves the rate of change of the unit tangent vector. Deriving the curvature starts with the equation of a circle. Then three equations that force the collocation circle to go through the three points and on the curve must be written down. Then solve for a, b, and r.
