Question Please answer a give ajustification for upvote thank you 5. Determine whether or not the following graph is planar. If it is, give a planar representa- tion. If it is not, explain why not. 04 U5 03 16 U2 V1

Find the solution to the linear system of differential equations x 0 = −3x+4y y 0 = −6x+7y satisfying the initial conditions x(0) = −7 and y(0) = −10. x(t) = y(t) = Find the solution to the linear system of differential equations (0) -10 de satisfying the initial conditions (0) -- and 6 + 7 a(t) (0)

(2 points) Evaluate the indefinite integrals using Substitution. (use C for the constant of integration.) ax) - (In 2) 8 dr = In(24) dc b) 2 oſ 1 InCr") dc

A simple 1-DOF mechanical system has the following transfer function: \[ G(s)=\frac{Y(s)}{U(s)}=\frac{0.25}{s^{2}+2 s+10} \] where position \( y(t) \) is in \( \mathrm{m} \). The system is initially at rest, \( y(0)=y(0)=0 \), and the applied force is a step function \( u(t)=4 U(t) \mathrm{N} \). Determine the system response using Laplace methods. Here, \( U(t) \) represents the unit step function.

02 Question (1 point) e See page 373 1st attempt hd See Periodic Table See Hint Do you expect the ionization energies of anions of group 17 elements to be lower than, higher than, or about the same for neutral atoms of the same group? Choose one: O higher than O lower than about the same SUBMIT ANSWER 02/14 >

7.22 A simple 1-DOF mechanical system has the following transfer function Y(s) 0.25 U(s) s +2s +9 where the position of the mass y0) is in meters. The system is initially at rest, y(O) (0) 0, and the applied force is a step function u(t0 4N Copyrighto Problems 243 a. Accurately sketch the system response y() and label all important performance criteria on your sketch b. Use MATLAB or Simulink to verify your sketch in part (a). Plot y(o) from the numerical solution. 7,22 A simple 1-DOF mechanical system has the following transfer function Ms), 2) 025 CO" Tg) * Be Ds+9 ‘where the position of the mass y(0) is in meters. The system i applied force is a step function u() = 4N, lially at rest, y(0) = 5(0) = 0, and the Copyrighte Problems 243 

Shown in the figure below is an electrical circuit containing three resistors and two batteries. 11 R1 ww 10 R2 ww 12 R3 Write down the Kirchhoff Junction equation and solve it for I, in terms of 12 and 13. Write the result here: 11 = Write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and follows the perimeter of the circuit diagram clockwise 0 = Write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and touches the components 4V, Rz, and Rz. 0 = The resistors in the circuit have the following values: • R = 120 • Ry=50 • Rg = 30 Solve for all the following (some answers may be negative) Amperes 12 - Amperes 13 Amperes NOTE: For the equations, put in resistances and currents SYMBOLICALLY using variables like R1, R2,R3 and 11,12,13. Use numerical values of 10 and 4 for the voltages