Q3 A. Consider the control process \begin{pmatrix}x\\ y\\ z\end{pmatrix}^'=\begin{pmatrix}0&1&0\\ 0&0&1\\ -2&-4&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix}+\begin{pmatrix}1&0\\ 0&1\\ -1&1\end{pmatrix}\begin{pmatrix}u_1\left(t\right)\\ u_2\left(t\right)\end{pmatrix}. Is this system glablly null controllable ? Use C = [B,AB] and use Echelon Form of C. Use this to solve Q3 B. Is the system in Q3 A gloabally null controllable under the additonal constraint ll \begin{pmatrix}u_1\left(t\right)\\ u_2\left(t\right)\end{pmatrix} ll \le 2 ?

Q: Find the following derivatives.   z_s and z_t​, where z = 6xy - 4x^2, x = 4s + t, and y = 4s+t​.

A:

Q: the derivative of E(q) is-(q*(q^2-1))^-1. what's its global maximum and global minimum. Thank you!

A:

Q: The method of u-substitution is the integral analog of the chain rule of derivatives and the method…

A: Let say we have two functions f(x) & g(x)Now combine the function f(g(x))Hence, the derivative…

Q: How do I find the gradient using exponential curve fitting? i.e. y = a*e^(b*x)

A:

Q: A carpenter wanted to predict how many pieces of furniture they could produce in a certain time…

A:

Q: Evaluate. t*dt

A: Evaluating the definite integral

Q: parameterize the curve that starts at (2,9) and follows function y=x^3+1 to end at the point…

A: Given the curve,  y=x3+1 Suppose,x(t)=t     ⇒ y(t) =t3+1 The parametric form of the equation is:…

Q: Sketch the graph of y=(x^2 +x +3)/x^2, locate all maximum and minimum values, intervals of increase…

A: we need to graph the given function and also need to find out the critical points, etc

Q: The equation x''+ x = sin t has a bounded solution. true or false ?

A:

Q: 3/ Find tangent line and Normal # line to the Curve 6x²³²+3x²³²y+2y² + 17y=6 at (-1,0) Also find the…

A:

Q: 39 Find the value of c that satisfies Rolle's theorem for f(x) = 2x^4 -16x I 5. You are a…

A: Given query is to find the the value of c.

Q: The Power Chain Rule simplifies computing the derivative of a powerof an expression

A: To find the derivative of a power of an expression using the chain rule. ddxe3x+1 Solution: Chain…

Q: Differentiate Find y' Show all work

A: y=3xlog3x

Q: part A. let C be a curve of points in R^2 which satisfy the equation  x^3 + xy +y^2 =3. use…

A: We will answer the first question since we answer only one question at a time. Please submit the…

Q: In experimental studies conducted on bacteria in the bioprocess laboratory, bacterial growth rate…

A: Step-by-step procedure to draw the fitted line plot using Excel: In Excel sheet, enter and select…

Q: If the equation of the regression line for hours xx  spent cycling in the summer and hours yy  spent…

A: The regression equation is given by y = -0.7x + 42 Where x = hours spent cycling  y = hours spent…

Q: If |z|=1,show that (z^-1) =(z congegate)

A: Given z=1 We have to show that z−1=z¯ Since, z=1 ⇒z2=1 We know that z2=zz¯

Q: Find the normal to the curve y = 1 – x² at the point (3, -8).

A:

Q: Determine the intervals of concavity and point of inflection of curve y=2x^4-3x^2+2x+1

A:

Q: Find the gradient of the function whose center is at the origin and radius of 7units…

A: We have to find gradient of the function whose center is at origin and radius of 7 units. We know…

Q: Show that the functions y1= e^t,  y2 = e^-t, and te^-t are linearly independent.

A:

Q: Use the gradient descent method in the equation f=2(x_1)^2 + (x_2)^2 with the starting point (1,2)…

A: Given : equation                fx1, x2=2x12+x22 with starting point 1, 2 Use gradient descent in…

Q: 3) A researcher has collected population data along with time. Afler comparing the populations from…

A: Solution is given below

Q: generate or sketch of graph y=6x^1/3+3y^4/3 and analyse it

A: Given function is y=6x13+3x43. We have to sketch the graph of the given function. Domain:- Since,…

Q: p5 _3ar4 +23r2 h (r) 4r2

A: Given that h(r)=r5-3αr4+2βr24r2 We need to find out derivative of h(r) respective to r.

Q: Find the directions in which f increases and decreases most rapidly at point P. Then find the…

A: Step:-1

Q: show that e^(4t-3t^2) cannot be a moment generating function

A: Moment Generating Function:                The Moment Generating Function is the expected value of…

Q: How to find stationary points for f(x) = x^2-6x^2+9x and their local max or local min

A:

Q: Evaluate the value of ‘a’ if the first derivative of m(x,y,z)=4-ax^2-2y^2, with respect to the…

A: Consider: mx,y,z=4-ax2-2y2 and mx1,2,3=-2. Solve for a. Calculate mxx,y,z by applying…