Time (s) Height (m) 0.5 1 1.5 2 3 11 17 21 23 18

A linear second-order non-homogeneous equation models this scenario: People falling at a height of 100ft above the ground attached to a 100-foot rope into a pit that's 25 ft deep and 75 feet from ground level. Spring constant of the rope is 120 lbs/ft, and air resistance is 5 times the instantaneous velocity. M is mass of person and g is gravity. Note that the pit is actually 100 ft in height: 75 from ground level plus 25 ft deep. Write this scenario as an initial value problem in matrix form. The equation is my''+5y'+120y=mg

A tire company has found that the quantity demanded x, in thousands of units per week, of their best-selling tire is related to the unit price p by the equation (see image). A.) Use differentials to find an approximate change in the quantity of tires demanded per week if the unit price of the tires is increased from $119 to $122 per tire. B.) Use your calculator to find the actual demand for tires when the price is set at $119 and $122 per tire. Then find the difference in demand. C.) Explain why the answers to parts A and B are not the same.

find the differentiate of h(t)= the 5th square root of t - 5e to the power of t

High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about 1.2 m/s², and (2) the typical maximum speed attainable is about 8.8 m/s. You board an elevator on a skyscraper's ground floor and are transported 190 m above the ground level in three steps: acceleration of magnitude 1.2 m/s² from rest to 8.8 m/s, followed by constant upward velocity of 8.8 m/s. then deceleration of magnitude 1.2 m/s² from 8.8 m/s to rest. T Part A Determine the elapsed time for each of these 3 stages. Express your answers using two significant figures separated by commas. tace, tconstant, tdec = Submit Part B AFN,acc AFN,constant FN FN Submit Request Answer 2 [5] ΑΣΦ Determine the change in the magnitude of the normal force, expressed as a % of your normal weight during each stage. Express your answers using two significant figures separated by commas. 2 AFN,dec FN Request Answer Part C Complete…

Fit a linear function of the form f (t) = c0 + c1t to the data points (0, 0), (0, 1), (1, 1), using least squares. Use only paper and pencil. Sketch your solution, and explain why it makes sense.

A pan of boiling water with a temperature of 212°F is set in a bin of ice with a temperature of 32°F. The pan cools to 65°F in 33 minutes. (a) Find To, D, and a so that T(t) = T₁ + Dat models the data, where t is in hours. (b) Find the temperature of the pan after 15 minutes. (c) How long did it take the pan to reach 35°F? Support your result graphically. (a) To (Round to the nearest integer as needed.) =

The "Yaw Damper System" provides airplane stabilization about the yaw axis. The Yaw Damper minimizes dutch roll during flight by providing rudder displacement proportional to, and opposing, the yaw rate of the airplane. Transfer function of the yaw damper is taken as: 4.833 yaw rate rudder angle (s+0.551)(s+0.1 ±0.541*i) (s+0.616)(s +0.058+ i)(s+0.007) a) Give a brief knowledge about yaw dampers. b) Draw and interpret "root-locus" graphic of this transfer function. c) Draw and interpret the yaw rate distribution according to time.

In a study conducted at Dartmouth College, mice with a particular type of cancerous tumor were treated with a chemotherapy drug called Cisplatin. If the volume of one of these tumors at the time of treatment is Vo, then the volume of the tumor t days after treatment is modeled by the function V(t) = = Vo(0.99e- + 0.01e0.239t). -0.1216t 1. Set Vo = 3 and plot V(t) over the interval 0 ≤ t ≤ 16. Appropriately adjust the viewing window to see the behavior of V(t) and sketch the graph below. 2. From the graph, estimate the time at which the volume of the tumor decreased to half its original amount. There are two such times, record each to the nearest whole number. 3. With Vo = 3, write down the equation whose solution gives the time at which the tumor is half its original volume. (Re)write the equation with zero in the right-hand side. 4. Using one of your answers from 2. as to and your equation from 3., apply two steps of Newton's method to better approximate this time. (Round to 3 decimal…

(b) Find the Linearization of the function: f(x)=Vx at a=27 and use it to approximate the number V27.04 (6