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In Problems 3-18, use the elimination method to find a general solution for the given linear system, where differentiation is with respect to
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Fundamentals of Differential Equations and Boundary Value Problems
- If y = x2 is one solution of x2y''+2xy'-6y=0 and the other linearly independent solution.arrow_forward5. Solve the following linear system: dX dt with the initial condition = [83] X (0) = -3 2 X Garrow_forwardA firm produces two types of calculators each week, x of type A and y of type B. The weekly revenue and cost functions (in dollars) are as follows. R(x,y)= 110x + 180y + 0.02xy – 0.07x2 – 0.04y? C(x,y) = 6x + 6y + 20,000 Find Px(1100,1800) and Py(1100,1800), and interpret the results.arrow_forward
- A firm produces two types of calculators each week, x of type A and y of type B. The weekly revenue and cost functions (in dollars) are as follows. R(x,y) = 120x + 170y + 0.03xy – 0.08x2 – 0.05y2 C(x,y) = 9x+ 3y + 20,000 Find P,(1200,1700) and P,(1200,1700), and interpret the results. Px(1200,1700) = O Choose the correct interpretation of P (1200,1700). O A. Selling 1,200 units of type A and 1,700 units of type B will yield a profit of approximately $30. B. Wen selling 1,200 units of type A and 1,700 units of type B, the profit will decrease approximately $30 per unit increase in production of type A. O C. Selling 1,200 units of type A and 1,700 units of type B will yield a profit of approximately $45. O D. When selling 1,200 units of type A and 1,700 units of type B, the profit will decrease approximately $45 per unit increase in production of type A. Py(1200,1700) =| Choose the correct interpretation of P,(1200,1700). O A. When selling 1,200 units of type A and 1,700 units of type B,…arrow_forwardA firm produces two types of calculators each week, x of type A and y of type B. The weekly revenue and cost functions (in dollars) are as follows. R(x,y) = 140x + 160y + 0.05xy – 0.09x2 – 0.03y2 C(x,y) = 9x+ 9y + 20,000 Find P,(1400,1600) and P,(1400,1600), and interpret the results. P(1400,1600) = Choose the correct interpretation of P(1400,1600). A. Selling 1,400 units of type A and 1,600 units of type B will yield a profit of approximately $41. B. When selling 1,400 units of type A and 1,600 units of type B, the profit will decrease approximately $51 per unit increase in production of type A. C. Selling 1,400 units of type A and 1,600 units of type B will yield a profit of approximately $51. D. When selling 1,400 units of type A and 1,600 units of type B, the profit will decrease approximately $41 per unit increase in production of type A. Py(1400,1600) = O %3D Choose the correct interpretation of Py(1400,1600). O A. Selling 1,400 units of type A and 1,600 units of type B will…arrow_forwardIf x/4 = y/3 = z/2, then what would be the value of (5x + y – 2z) / 3yarrow_forward
- Thus far in the class we've only seen one kind of so-called "linear" difference equation models: the Malthusian ones of the form N(t+1)= XN (t) This is called linear because N(t+1) is a linear function of N(t) - in other words, if we view N(t+1) as "y" and N(t) as "r" then this is an equation of the form "y = mx" since À is a constant. Another more general type of "linear" difference equation is: N(t+1) = AN(t) + a where a is some constant. This is again a linear model because N(t+1) is a linear function of N(t), this time of the form "y=mx+b". This is sometimes called a "linear difference equation with a constant term". The next few problems have to do with linear difference equations with constant terms. 4. Consider the difference equation N(t + 1) = 0.5N(t) + 40 where we are given that N(0) = 100. a) Check that N(t) = 100* (0.5) is not a solution to this difference equation. b) Check that N(t) = 100* (0.5) +40 is not a solution to this difference equation. c) Check that N(t) = 20 *…arrow_forward7. Express the general solution to the following system in terms of real- 30-2 -1 1 0 210 valued functions: x': = 8³] X.arrow_forwardA firm produces two types of calculators each week, x of type A and y of type B. The weekly revenue and cost functions (in dollars) are as follows. R(x,y)=130x+160y+0.02xy−0.08x2−0.03y2 C(x,y)=2x+4y+30,000 Find Px(1300,1600) and Py(1300,1600), and interpret the results. Px(1300,1600)= Choose the correct interpretation of Px(1300,1600). A. When selling 1,300 units of type A and 1,600 units of type B, the profit will decrease approximately $54 per unit increase in production of type A. B. When selling 1,300 units of type A and 1,600 units of type B, the profit will decrease approximately $48 per unit increase in production of type A. C. Selling 1,300 units of type A and 1,600 units of type B will yield a profit of approximately $48. D. Selling 1,300 units of type A and 1,600 units of type B will yield a profit of approximately $54. Py(1300,1600)= Choose the correct interpretation of Py(1300,1600).…arrow_forward
- 5. Give the graphical significance of the constant a for the equations of the form y-a(x-h)²+k.arrow_forwardProblem 4. The equation x +xy+y² =3 implicitly defines y as a function of x. Note that (x = 1, y = 1) is a solution of the equation. Using a linear approximation that makes use of the point (1, 1), the approximate value of y when x= 1.1 is (A) 43/40 (B) 1 (C) 5/6 (D) 25/40 (E) none of the other choices is correctarrow_forwardA firm produces two types of calculators each week, x of type A and y of type B. The weekly revenue and cost functions (in dollars) are as follows. R(x,y)=140x+170y+0.06xy−0.09x2−0.06y2 C(x,y)=6x+9y+30,000 Find Px(1400,1700) and Py(1400,1700), and interpret the results.arrow_forward
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