The value of the expression is true or 1.
The values of x,y and z are as shown in the question.
The expression uses AND operation.
So the result of the expression is true if both conditions are true.
y>=6 is true.
z<-1 is true.
So the result of the expression is true.
Let z=5 where x, y, z E R. Prove that z? +z2+z?>
where 7 is the region defined by >0, y >0, >0, r+y+z<3.
Problem 5 If z and y are positive, then > V2+y Answer:
3. Suppose x,y,z satisfy the competing species equations <(6 - 2x – 3y - 2) y(7 - 2x - 3y - 22) z(5 - 2x - y -22) (a) (6 points) Find the critical point (0,Ye, ze) where ye, we >0, and sketch the nullclines and direction arrows in the yz-plane. (b) (6 points) Determine if (0, yc, ze) is stable. (c) (8 points) Determine if the critical point (2,0,0) is stable, where I > 0.
If X is Rayleigh distributed amplitude with an average power of 10, what is the pdf of Y-1-exp(-XA2/10)? If X is N(0,4) and Y is N(0,9) and X and Y are independent, what is the prob (XY>0)?
5. (10 points) Let p="x < y", q="x < 1", and r="y > 0". Using ~, 1, V write the following statements in terms of the symbols p, q, and r. (a) 0 <y < x < 1. (b) 1 < x <y<0.
5. Let F(x, y, z) = (yz, xz, xy) and define Cr,h = {(x, y, z) : x2 + y2 = p2, z = h}. 1 Show that for any r > 0 and h ER, Sony F. dx = 0
2. a) Solve the initial value problem dy 1 dx 1+2x y -2x+1:y(2)-5 b) Explain why this solution is defined for all x >-
3) Given vector field F(x,y,z)=<y, xz,x? >. Find N dr where T is the path around the triangle with vertices (1,0,0),(0,1,0) and (0,0,1) traced counterclockwise (when viewed from above.)
96. Consider a vector field F(x, y, z) =< x + x cos(yz), 2y - eyz, z- xy > and scalar function f(x, y, z) = xy3e2z. Find the following, or explain why it is impossible: a) gradF (also denoted VF) b) divF (also denoted .F) c) curl(f) (also denoted xf) d) curl(gradf) (also denoted V x (0f) e) div(curlF) (also denoted 7. (V x F))