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The temperature at a point (x, y) is T(x,y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = 4 + t, y = 8 where x and y are measured in centimeters. The temperature function satisfies Tx(5, 9) = 2 and Ty(5, 9) = 7. How fast is the temperature rising on the bug's path after 21 seconds? Step 1 We know that the rate of change of the temperature...
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1) 2D kinematics (rectangular coordinates) - A particle moving in the x-y plane has an acceleration in the y-direction given as ay -3t ft/s2 and an x-position ofx 3t + 2 ft. When t0, yo3ft and Vo, -4ft/s. a) Derive expressions for x, vx, ax, V, Vy, ay as functions of time. b) At times t 0,1,2 seconds, calculate the magnitude of velocity and the angle it makes with the x-axis. c) At times t 0,1,2 seconds, calculate the magnitude...
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John has been hired to design an exciting carnival ride. Tiff,
the carnival owner, has decided to create the world's greatest
Ferris wheel. Tiff isn't into math; she simply has a vision and has
told John these constraints on her dream: (i) the wheel should
rotate counterclockwise with an angular speed of a = 12
RPM; (ii) the linear speed of a rider should be 200 mph; (iii) the
lowest point on the ride should be c = 3 feet...
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Problem 2 An RC circuit ( with an active component) has the following transfer function (where R and Care positive) H(s) - Vout(8) _R|| R/10k12 Vin(8) 10KN 1 + $RC Where s = jw Find the value of the resistor and the value of the capacitor so that: for w = 0 rad/s, H(jw)lde = +12dB at f = 1kHz, |H(jw)lab = +9dB Problem 3 The transfer function of a circuit is given by H(S) = Vout(s) Vin(s) Where s...
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1. An airplane if flying horizontally at a constant height of 6 km above a fixed observation point. At a certain moment the angle of elevation θ is 30° and decreasing and the speed of the plane is 4 km/h. (a) How fast is 0 decreasing at this moment? (b) How fast is the distance between the plane and the observation point is changing at this moment? 2. Trajectory of a particle is described by parametrical equations as t,y P,...
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When an object is dropped straight down, the distance in feet) that it travels in t seconds is given by s(t) = - 1612. Find the velocity at each of the following times. a. After 2 seconds. b. After 6 seconds. c. After 10 seconds. d. Find the acceleration. a. The velocity after 2 seconds is ft/sec. Sketch the graph of the given function by determining the appropriate information and points from the first and second derivatives. y = x2...
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An object is moving around the unit circle with parametric
equations x(t)=cos(t), y(t)=sin(t), so it's location at
time t is P(t)=(cos(t),sin(t)) . Assume 0
< t < π/2. At a given time t, the tangent line
to the unit circle at the position P(t) will determine a
right triangle in the first quadrant. (Connect the origin with the
y-intercept and x-intercept of the tangent
line.)
(a) The area of the right triangle is
a(t)= .
(b)
lim t →
pi/2−a(t)=
...
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(1 point) In your answers below, for the variable i type the word lambda, for y type the word gamma; otherwise treat these as you would any other variable. We will solve the heat equation u, = 4uxx: 0<x<2, 120 with boundary/initial conditions: u(0,1) = 0, and u(x,0) = So, 0<x< 1 u(2, 1) = 0, 13, 1<x<2. This models temperature in a thin rod of length L = 2 with thermal diffusivity a = 4 where the temperature at...
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1. A picture of a solar tower is shown below (figure 1). You can see that there are plenty of mirrors located in different positions. Each of these mirrors tracks the sun over time and project the sunlight to the tower. The tower gets very hot and the heat is used to generate electricity (or to evaporate water). To make this problem easier for you, I changed this problem to a 2D example. 4 Figure 1 Solar Tower Figure 2...
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P4.2: The four-bar mechanism in Figure P4.2 has the link lengths: LAB = 4", LED = 24", Loc = 14", LA = 30". The location of COM is as follows: LAG = 2.120"; LEG2 = 11.863"; LDG = 6.722". The crank 1 rotates counterclockwise with the angular displacement 8. = 27t-t [rad), angular velocity 0. = , = 21 [rad/s], and angular accelera- tion &= 7= 0 [rad/s). The mass and moment of inertia relative to each link's COM are...
The temperature at a point (x, y) is T(x,y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = 4 + t, y = 8 where x and y are measured in centimeters. The temperature function satisfies Tx(5, 9) = 2 and Ty(5, 9) = 7. How fast is the temperature rising on the bug's path after 21 seconds? Step 1 We know that the rate of change of the temperature...
1) 2D kinematics (rectangular coordinates) - A particle moving in the x-y plane has an acceleration in the y-direction given as ay -3t ft/s2 and an x-position ofx 3t + 2 ft. When t0, yo3ft and Vo, -4ft/s. a) Derive expressions for x, vx, ax, V, Vy, ay as functions of time. b) At times t 0,1,2 seconds, calculate the magnitude of velocity and the angle it makes with the x-axis. c) At times t 0,1,2 seconds, calculate the magnitude...
John has been hired to design an exciting carnival ride. Tiff,
the carnival owner, has decided to create the world's greatest
Ferris wheel. Tiff isn't into math; she simply has a vision and has
told John these constraints on her dream: (i) the wheel should
rotate counterclockwise with an angular speed of a = 12
RPM; (ii) the linear speed of a rider should be 200 mph; (iii) the
lowest point on the ride should be c = 3 feet...
Problem 2 An RC circuit ( with an active component) has the following transfer function (where R and Care positive) H(s) - Vout(8) _R|| R/10k12 Vin(8) 10KN 1 + $RC Where s = jw Find the value of the resistor and the value of the capacitor so that: for w = 0 rad/s, H(jw)lde = +12dB at f = 1kHz, |H(jw)lab = +9dB Problem 3 The transfer function of a circuit is given by H(S) = Vout(s) Vin(s) Where s...
1. An airplane if flying horizontally at a constant height of 6 km above a fixed observation point. At a certain moment the angle of elevation θ is 30° and decreasing and the speed of the plane is 4 km/h. (a) How fast is 0 decreasing at this moment? (b) How fast is the distance between the plane and the observation point is changing at this moment? 2. Trajectory of a particle is described by parametrical equations as t,y P,...
When an object is dropped straight down, the distance in feet) that it travels in t seconds is given by s(t) = - 1612. Find the velocity at each of the following times. a. After 2 seconds. b. After 6 seconds. c. After 10 seconds. d. Find the acceleration. a. The velocity after 2 seconds is ft/sec. Sketch the graph of the given function by determining the appropriate information and points from the first and second derivatives. y = x2...
An object is moving around the unit circle with parametric
equations x(t)=cos(t), y(t)=sin(t), so it's location at
time t is P(t)=(cos(t),sin(t)) . Assume 0
< t < π/2. At a given time t, the tangent line
to the unit circle at the position P(t) will determine a
right triangle in the first quadrant. (Connect the origin with the
y-intercept and x-intercept of the tangent
line.)
(a) The area of the right triangle is
a(t)= .
(b)
lim t →
pi/2−a(t)=
...
(1 point) In your answers below, for the variable i type the word lambda, for y type the word gamma; otherwise treat these as you would any other variable. We will solve the heat equation u, = 4uxx: 0<x<2, 120 with boundary/initial conditions: u(0,1) = 0, and u(x,0) = So, 0<x< 1 u(2, 1) = 0, 13, 1<x<2. This models temperature in a thin rod of length L = 2 with thermal diffusivity a = 4 where the temperature at...
1. A picture of a solar tower is shown below (figure 1). You can see that there are plenty of mirrors located in different positions. Each of these mirrors tracks the sun over time and project the sunlight to the tower. The tower gets very hot and the heat is used to generate electricity (or to evaporate water). To make this problem easier for you, I changed this problem to a 2D example. 4 Figure 1 Solar Tower Figure 2...
P4.2: The four-bar mechanism in Figure P4.2 has the link lengths: LAB = 4", LED = 24", Loc = 14", LA = 30". The location of COM is as follows: LAG = 2.120"; LEG2 = 11.863"; LDG = 6.722". The crank 1 rotates counterclockwise with the angular displacement 8. = 27t-t [rad), angular velocity 0. = , = 21 [rad/s], and angular accelera- tion &= 7= 0 [rad/s). The mass and moment of inertia relative to each link's COM are...