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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.Find a control function u(t) : [0, infinity) -> R such that (1) l u(t) l smaller than or equal to 2 for all t in [0, infinity) and (2) u steers \begin{pmatrix}1\\ 1\end{pmatrix} to \begin{pmatrix}0\\ 0\end{pmatrix} where the control system is given by \begin{pmatrix}x\\ y\end{pmatrix}^'=\begin{pmatrix}0&1\\ -1&0\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}+\begin{pmatrix}0\\ 1\end{pmatrix}u\left(t\right). Use Analysis to solve the problem.The number of defects on the front side (X) of a wooden panel and the number of defectsa on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy(x,y)=c(x+y), x= 1,2,3 and y=1,2,3. Determine the value of c.
- Find a control function u(t) : [0,infinity) -> R such that (1) l u(t) l smaller than or equal to 2 for all t in [0,infinity) and 2) u steers \begin{pmatrix}1\\ 1\end{pmatrix} to \begin{pmatrix}0\\ 0\end{pmatrix} where the control system is given by \left(\begin{pmatrix}x\\ y\end{pmatrix}\right)^' = \begin{pmatrix}0&1\\ -1&0\end{pmatrix} \begin{pmatrix}x\\ y\end{pmatrix} + \begin{pmatrix}0\\ 1\end{pmatrix} u(t)Consider an experiment in which a subject performs a task while being exposed to two different stiumli (for example, sound and light). For low levels of the stimuli, the subject's performance might actually improve, but as the stimuli increase, they eventually become a distraction and the performance begins to deteriorate. Suppose in a certain experiment in which x unites of stimulus A and y unites of stimulus B are applied, the performance of a subject is measured by the funtion f(x,y) = C+xye(1-x^2-y^2) where C is a positive constant. How many units of each stimulus result in maximum performance?dik koordinatylarda x,y öyleki x kare artı y kare küçüktür beş denkleminin grafiğini çiziniz
- The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy (x,y)=c(x+y), x=1,2,3 and y=1,2,3. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent.Find a control function u(t) : [0, infinity) -> R such that (1) l u(t) l smaller than or equal to 2 fr all t in [0, infinity) and (2) u steers \begin{pmatrix}1\\ 1\end{pmatrix} to \begin{pmatrix}0\\ 0\end{pmatrix} where the control system is given by \begin{pmatrix}x\\ y\end{pmatrix}^'=\begin{pmatrix}0&1\\ -1&0\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}+\begin{pmatrix}0\\ 1\end{pmatrix}u\left(t\right).Find a control function u(t) : [0, infinity) -> R such that (1) l u(t) l smaller than or equal to 2 fr all t in [0, infinity) and (2) u steers \begin{pmatrix}1\\ 1\end{pmatrix} to \begin{pmatrix}0\\ 0\end{pmatrix} where the control system is given by \begin{pmatrix}x\\ y\end{pmatrix}^'=\begin{pmatrix}0&1\\ -1&0\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}+\begin{pmatrix}0\\ 1\end{pmatrix}u\left(t\right). Use Analysis to solve the problem but no code.
- a). Deternine if the DE is classified as Variable Seperable DE or Homogeneous DE. If the DE is Homogeneous, what is the degree of homogenity? b). Find the general solution of the DE shown.Compare truncation and round-off error.Compute the maximum relative error in u when x = y = z = 1, if u=4x2y3/z4 and errors in x, y, z be 0.001.A manufacturing company employs two devices to inspect output for quality controlpurposes. The first device can accurately detect 99.2% of the defective items it receives, whereasthe second is able to do so in 99.5% of the cases. Assume that five defective items are producedand sent out for inspection. Let X and Y denote the number of items that will be identified asdefective by inspecting devices 1 and 2, respectively. Assume that the devices are independent.Find: a. f Y|2(y) b. E(Y│X=2)= and V(Y│X=2)=