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- Show that t, e^t, and sin(t) are linearly independent.Find an equivalent dyadic position for each given Hackenbush posi- tion: "Y (a) (b) (c) (d)Determine which of the following pairs of functions are linearly independent. NO_ANSWER v 1. f(0) = cos(30) g(0) = 16 cos (0) – 12 cos(0) NO_ANSWER v 2. f(t) = 4t² + 28t g(t) = 4t2 – 28t
- A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the dining table. At this same time the cup of tea is cooling at a rate of 15 °F/min. 3) а) Give the local linearization, L(x), to T at t = 1. Show all work clearly.Consider the Squirrel-Coyote system given by S' = 2S-4SC C' = SC-C (1) Sketch the nullclines of the system and label them (as S- or C-nullclines). Add arrows to each nullcline and each distinct region of the phase plane to indicate the direction of the vector field there. (No need to draw the whole vector field, just a single arrow to show direction in each significant place.)The cantilever beam shown in Figure 2.1 is subjected to linearly distributed loads. a) Draw all necessary free-body diagrams using the method of sections and find symbolic expressions for the internal shear force (V(x)) and bending moment (M(x)) due to the external forces as functions of x, where x is a horizontal coordinate along the length of the beam, measured from the most left support of the beam. Your expression(s) must allow to obtain internal reactions for 0Hi, I posted this previously but the work wasn’t properly attached. If you could help me out I would appreciate it! :)Let W be the work (against the Sun’s gravitational force) required to transport an 80-kg person from Earth to Mars when the two planets are aligned with the Sun at their minimal distance of 55.7 × 106 km. Use Newton’s Universal Law of Gravity (see Exercises 35–37 in Section 6.5) to expressW as an integral and evaluate it. The Sun has massMs = 1.99×1030 kg, and the distance from the Sun to Earth is 149.6×106 km.find the Fourier transform of given signal x(t) = 1/(a²+t²)what are the stable equilibria (X1 ,X2)?Find the DFT of [1, 2, 0].Consider a spring-mass system that has a 15 kg mass, a damping coefficient of 45 N/m², and a spring that, when stretched 0.4 m, imposes a force of 12 N. a.) Explain why the spring constant is 30 N/m. 45 b.) These values lead to the equation, y + 15y + 3y = 0, assuming no forcing function is present. Solve for the position as a function of time by using an appropriate guess. Be sure to show all work. (You can round to two decimal places, e.g., 94.3453 = 94.35) c.) Now, suppose we incorporate a forcing function of e-2t, such that our equation becomes y" + 3y + 2y = e 2t. We might imagine our particular guess to be of the form ae 2t, however, it will not work in this case. So, use a guess of the form ypat e 2t. With this, apply the Linearity Principle to find the general solution to this nonhomogeneous ODE.