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Differential Equations and Linear Algebra (4th Edition)
- If the quantities x and y are related by the equation y=3x , then we say that y is __________ _________ to x and the constant of ____________ is 3.arrow_forwardUse a system of linear equation to find the parabola y=ax2+bx+c that passes through the points (1,2), (0,1) and (2,6)arrow_forwardFind a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.arrow_forward
- Apply the method of undetermined coefficients to find a particular solution to the following system. - 3t x' = 7x- 10y + 12, y' = 2x- 5y - 2 e ..... Xp (t) =arrow_forwardCompute the general solution for the following equationarrow_forwardTanks 1 and 2 contain 50 gallons and 100 gallons of salt solutions. T1 and T2. A solution with 5/2 pounds of salt per gallon is pumped into Tank 1 at 1 gallon per minute. From an external source. A solution with 7/2 pounds of salt per gallon is pumped into Tank 2 at 2 gallons per minute. From an external source. The solution is then pumped from T1 to T2 at 2 gallons a minute. The solution is also pumped from T2 to T1 at 3 gallons a minute. T1 is then drained at 1 gallon a minute. T2 is drained at 2 gallons a minute. Let S1(t) and S2(t) represent the number of pounds of salt respective to t>0 Find the system of equations for Q1 and Q2. The help is appreciated.arrow_forward
- For the following system of nonlinear equations, give all solutions, including any non-real complex solutions. x² – 4y? = 3 - xy = 1 O {(-2, –}), (2, ±), (-i,i), (i,–i)} O {(-;,-2), (;,2), (-i, i), (i,-i)} O {(-1, –1), (1, 1), (-2i, 2i), (2i, –2i)} O {(-÷,-), (;. 4) , (-2i, 31), (3i, –2i)}arrow_forwardGive the solution of (2x + 3y + z = −1 3x + 3y + z = 1. (2x + 4y + z = -2arrow_forwardThe concentrations of glucose and insulin in an individual interact with each other and vary over time. A mathematical model for the concentrations of insulin and glucose in an individual is given by the system x = x1 + 3 x2 x2 = 4 x1 + 5 x2 Find the general solution for this system. Then find the formula for = 2 and x2(0) x1(t) and x2 (t) if x1 (0) = 1.arrow_forward
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- Intermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell