Problems
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Differential Equations and Linear Algebra (4th Edition)
- 1. If rxty = +1 and rx2y = -1, can you tell what happens to rxy when we combine x1 and x2 into a new variable? Make and provide your own data for your demonstration.arrow_forward7. Find the following derivatives. z and z, wherez= 3xy-5x y, x=s+ 2t, and y = s-2t dz %3D (Type an expression using x and y as the variables.) %3D ds (Type an expression using s and t as the variables.) dy (Type an expression using x and y as the variables.) dy ds (Type an expression using s and t as the variables.) %3D (Type an expression using s and t as the variables.) dy %3D (Type an expression using s and t as the variables.) Zs = (Type an expression using s and t as the variables.) %3D (Type an expression using s andt as the variables.)arrow_forwardt2y″ − 4ty′ + 4y = 0arrow_forward
- A. Eliminate the arbitrary constants for the following: 1. 5x?y3 – 2xy* = -7c 3x²y – mx = 3 3. у %3D 2х — се* - Cze+ |arrow_forwardStep 4. Undo the change of variables u = u(x) in your answer to question 3 to calculate | 2xV4 + x² dx. Then select your answer from the options below. a. 1 3/2 4+ 3x b. (4 + x²)-2 + C 1 -1/2 2 글 (4 + x2) 12 + C d. (4 + x²) *2 + C 3/2 С. 3 3/2 3arrow_forwardIf 3x = 9y and 27y = 81z, find x/z?arrow_forward
- -1 -1 0 4 0 2. X 4 W A = B = and C = 1 2 -1 -2 -1 zr 2 А - В + сarrow_forward2x Evaluate / dx 2x+3 3log(2x+3) + C х — -2 ох- 3log(2x + 3) + C Ο None O 3log(2x+3) + C X - 2arrow_forwardIf find az/au and az/av. ?z/?u Əz/dv = z = sin(x² + y²), x = u cos(v), y = u sin(v), REMARK. This problem is unusual: the system expects simplified answers. For example, if the correct answer is a function of u and v identically equal to 1, then the expression exp(uv) *exp(-uv) would not be accepted, while the constant 1 would be. HINT. Try to simplify the *function* itself before differentiating it.arrow_forward
- .2 dt t2 + 1arrow_forward(i) Find the solution set of the following equations: 2 log, x-3log, y=7 and log, x-2log, y = 4 (ii).Given that log, (y-1)+ log, 2. = z and log, (y+1)+ log, x z-1, Show that y 1+8 and find the possible value(s) of y and x when z=1arrow_forwardFind the characteristics of x²r + 2xys + y²t = 0arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,