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10.A car's suspension can be modeled by 5000x" + 30000x' + 45000x = 0 . Find...
Each of the main cables supporting a suspension bridge can be roughly modeled as a one-dimensional...
Each of the main cables supporting a suspension bridge can be roughly modeled as a one-dimensional string of length 300 m, with a mass of 7.5 times 10^6 kg, placed under tension of 10 MN (Mega-Newtons)= 1.0 times 10^7 N. Suddenly, an earthquake creates a transverse wave in the cable with an amplitude of 1.60 m. a. What is the wave speed? b. If the earthquake drives the wave with a frequency 1.3Hz, what is the wavelength? c. What is...
A wave is modeled with the function y ( x , t ) = 0 ....
A wave is modeled with the function y ( x , t ) = 0 . 2 5 cos ( 0 . 3 0 x − 0 . 9 0 t + π/ 3 ) where all lengths are in meters and all times in seconds. a. Find the wavelength of the wave. b. Find the period of the wave. c. Find the wave speed (a positive number). d. What is the instantaneous velocity of one of the particles that...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be model...
Please i need help with question 4 and 5
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and x(t) is the downward displacement of...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be model...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system. r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by dt m dt m where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and r(t) is the downward displacement of the mass. 2. Find the...
1. Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know...
1. Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature for the day is 82 degrees and the low temperature of 68 degrees occurs at 3 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. D(t)= 2. A population of rabbits oscillates 18 above and below an average of 62 during the year, hitting the lowest value in January...
4. The time, t, that a butterfly lives after emerging from its chrysalis can be modeled...
4. The time, t, that a butterfly lives after emerging from its chrysalis can be modeled by the probability function 36 20 0, otherwise f(t) , where t is measured in days. a. Sketch the graph of f(t). (What are the x- and y axes labels?) b. Shade the region on your graph that represents the probability that a butterfly will die within 7 days of emerging. c. Compute the probability that a butterfly will die within 7 days of...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and x(t) is the downward displacement of the mass. 2. Find the homogenous solution, xh, to...
of this species can be modeled by the following function, where is the number of years...
of this species can be modeled by the following function, where is the number of years A species of fish was added to a lake. The population size P time the species was added to the lake. 2000 PC- 1+7-021 Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary Initial population size: fish Population size after 9 years: fish x 5 ? Let o...
The demand for a new computer game can be modeled by p(x) = 58 -8 In...
The demand for a new computer game can be modeled by p(x) = 58 -8 In x, for 0 5x5 800, where p(x) is the price consumers will pay, in dollars, and x is the number of games sold in thousands. Recall that total revenue is given by R(x)=x.p(x). Complete parts (a) through (c) below. a) Find R(x). R(x) = b) Find the marginal revenue, R'(x). R'(x)=0 c) How many units will be sold if the price that consumers are...
The demand for a new computer game can be modeled by p(x) = 58 -8 In...
The demand for a new computer game can be modeled by p(x) = 58 -8 In x, for 0 5x5 800, where p(x) is the price consumers will pay, in dollars, and x is the number of games sold in thousands. Recall that total revenue is given by R(x)=x.p(x). Complete parts (a) through (c) below. a) Find R(x). R(x) = b) Find the marginal revenue, R'(x). R'(x)=0 c) How many units will be sold if the price that consumers are...
Each of the main cables supporting a suspension bridge can be roughly modeled as a one-dimensional string of length 300 m, with a mass of 7.5 times 10^6 kg, placed under tension of 10 MN (Mega-Newtons)= 1.0 times 10^7 N. Suddenly, an earthquake creates a transverse wave in the cable with an amplitude of 1.60 m. a. What is the wave speed? b. If the earthquake drives the wave with a frequency 1.3Hz, what is the wavelength? c. What is...
Please i need help with question 4 and 5
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and x(t) is the downward displacement of...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system. r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by dt m dt m where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and r(t) is the downward displacement of the mass. 2. Find the...
4. The time, t, that a butterfly lives after emerging from its chrysalis can be modeled by the probability function 36 20 0, otherwise f(t) , where t is measured in days. a. Sketch the graph of f(t). (What are the x- and y axes labels?) b. Shade the region on your graph that represents the probability that a butterfly will die within 7 days of emerging. c. Compute the probability that a butterfly will die within 7 days of...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and x(t) is the downward displacement of the mass. 2. Find the homogenous solution, xh, to...
of this species can be modeled by the following function, where is the number of years A species of fish was added to a lake. The population size P time the species was added to the lake. 2000 PC- 1+7-021 Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary Initial population size: fish Population size after 9 years: fish x 5 ? Let o...
The demand for a new computer game can be modeled by p(x) = 58 -8 In x, for 0 5x5 800, where p(x) is the price consumers will pay, in dollars, and x is the number of games sold in thousands. Recall that total revenue is given by R(x)=x.p(x). Complete parts (a) through (c) below. a) Find R(x). R(x) = b) Find the marginal revenue, R'(x). R'(x)=0 c) How many units will be sold if the price that consumers are...
The demand for a new computer game can be modeled by p(x) = 58 -8 In x, for 0 5x5 800, where p(x) is the price consumers will pay, in dollars, and x is the number of games sold in thousands. Recall that total revenue is given by R(x)=x.p(x). Complete parts (a) through (c) below. a) Find R(x). R(x) = b) Find the marginal revenue, R'(x). R'(x)=0 c) How many units will be sold if the price that consumers are...
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