az 6) Find and when s = = 1 and t = 2 for the following functions: z = x3 + x?y*, x = st”, y=8²t
Find and when s = 1 and t = 2 for the following functions: z = x3 + x^y^, x = st”, y = sat
6. [-12 Points] DETAILS SCALCET8 14.5.012. Use the Chain Rule to find Oz/os and Oz/t. z = tan(u/v), u = 6 + 9t, v = 9s - 6t дz as oz at Need Help? Read It Talk to a Tutor 7. [-13 Points] DETAILS SCALCET8 14.5.021. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x = 5 + 2t - u, θz oz oz when s = 4, t = 3, u =...
10. Assume that all variables are implicit functions of time t. Find the indicated rate. *2 + 5y2 + 4y = 69; * = 13 when x=6 and y= - 3; find y (Simplify your answer.)
Find the state equations for the following differential equation: dy(t) dy(t) + 6y(t) = z(t) dt3 dt2 dt +60360) + 11. 1 1 + oz(t) 0 0 -6 -11 X3 X 1 y(t) = [1 0 0] x2 + [0]z(t) X3 X1 0 1 0 = 0 0 0 X2 0 Iz(t) X2 6 11 6 X3 X3 X1 y(t) = [1 1 0] x2 + [O] z (t) X3
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for all X, Y E P (s), (X, Y) E R if and only if IX-T] = IY-T]. (a) Prove that R is an equivalence relation. (b) How many equivalence classes are there? Explain. (c) How mauy elements of [ø], the equivalence class of ø, are there? Explain (d) How many elements of [f1,2,3, 4)], the equivalence class of (1,2,3,...
(6) Let T R R² be defined by T (a, az) = (a, -a2, a., 29, +a). Let ß be the standard basis for 1R² and v= {(1,1,0, (0, 1, 1), (2, 3,3)} Compute [7]} .
(1 point) f(az +by), ie the RHS is a inear function of z and y We wil use the substtution oaz+ by to find an impict general solution In case an equation is in the form +yo sove the initial value problem. The right hand side of the following first order problem is a linear function of az and y Use the substitution sin(a+) We obtain the following separable equation in the varables z and t 1-sin and use cos...
Find the response of y(t) when x(t) = 3cos(7t+45degrees) and H(s) = 6/(2s+1)
ri 0 2-t] 3. Let Az = 0 t 1 .v= 10 0 2 (1) Find all possible t such that A, has determinant 1. (7 po (2) Find all possible t such that v is in the row space of Aų. (3) Find all possible t such that v is in an eigenspace of Al.