The velocity in m>s of an object moving alonga line over the time interval [0, 6] is v(t) = t2 + 3t. Find theaverage velocity of the object over this time interval.

Q: A particle moves along the x-axis so that at time t > 0 its position is given by x(t) = t – 24t.…

A: This is an application of differential calculus.

Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 10 x = 160 when p = $1…

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Q: Find the function "y" that makes the integral stationary V1+y²y2

A: Please check step 2 for solution

Q: Answer part D.

A: As we consider the approximation of function have already done in  above parts,(D) When change in x…

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = -3t2 - 2t +…

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Q: The position of a particle at time t is s(t) = t3 + t. Compute the average velocity over the time…

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Q: A wrench dropped from a state of rest at time t = 0 travels a distances(t) = 4.9t 2 mint seconds.…

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Q: Lets assume that y(t) represents how many fish are harvested in month t. Solve dy/dt =1/(y+yt2) with…

A: The given differential equation is: dydt=1y+yt2 and y0=4 Here t in month To find approximately how…

Q: Given y = V4x + 5, find the differential dy when a = 7 and dæ = 0.3. %3| Round your answer to three…

A: Given data:   The expression for the given function is y=(4x+5)1/2. The given value of x is x=7. The…

Q: Solve the initial-value problem for a as a function of t . dx (t² – 6t + 5). = 1, (t > 5, x(8) = 0)…

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Q: the maximum velocity attained on the interval 0 ≤ t ≤ 5 by the particle whose displacement is given…

A: Given that: displacement, s(t)=2t3-12t2+16t+2

Q: A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=t3−6t2+9t. Over…

A: A particle is moving along the y-axis its position is given by y(t)=t3-6t2+9t      at…

Q: Q9/ use the chain rule to express dy/dx in terms of x and y and choose correct answer. 1 x = t2 at t…

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Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: The acceleration of a particle is a(t) = 60t −4t3 m/s2. Compute the average acceleration and the…

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Q: Let v(t) = -13t + t² be the velocity, in ft/sec, of an object at time t, in seconds. a) What is the…

A: Given velocity function, v(t)= -13t + t²

Q: The position of a particle at time tis s(t) = 2t 3• Compute the average velocity over the time…

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Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 3t2 – 60t.…

A: v(t)=3t2-60t,    t≥0the particle is moving to the right whenv(t)>03t2-60t>03t(t-20)>0

Q: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting at t…

A: Given: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting…

Q: Solve the initial-value problem for x as a function of t. da (2t3 – 2t? +t – 1) 9, x(2) = 0 %3D dt

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Q: Show that for an object falling according to Galileo’s formula, the average velocity over any time…

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Q: d) Prove that the rate of growth, dt is given by NP (500 N) %3D dt 4000

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Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

Q: If a baseball is thrown upward with a velocity of 45 m/s, its height in meters t seconds later is…

A: We know that, Average velocity          = change in position/time elapsed.

Q: A particle moves along the x-axis so that at time t\ge 0t≥0 its position is given by…

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Q: A particle moves on a vertical line so that its coordinate at time t is y = t³ – 12t + 3,t > 0,…

A: Speeding up and slowing down is depend on the acceleration of particles so first find the…

Q: The position of a moving particle is given by s(t) = t2 – 2t + 6 on the interval 0 <t < 6, - where…

A: We will solve the following.

Q: A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s^2 is…

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Q: A particle moves along the x-axis so that at time t ≥ 0, its position is given by x(t) = 2t3 - 3t2.…

A: V(t) = d[x(t)]/dt Put, v(t) &gt; 0.

Q: Given the function s(t)= -16t2 + 128t, what is the average velocity at time interval [1,2]? Then…

A: The given function is,

Q: A particle moves along the x-axis so that at time t> 0 its position is given by x(t) = -t3 +11t?…

A: For the given position vector  x(t) = -t3+11t2-24t Velocity at t = 7 is calculated as shown below

Q: (b) If a rock is thrown upwared on the planet mars with a velocity of 12ms, its height in meters t…

A: The height of the rock is given by: y(t)=12t-1.92t2 To find the average velocity over the interval…

Q: Show steps please.

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Q: Find the maximum rate of change of f(s,t)=te^(st) at the point (0,−5).

A: We have to solve

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

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Q: A particle moves along the x-axis with velocity given by v(t) = 10t + 12 for time t> 0. If the…

A: Given: The velocity of the particle along x-axis is vt=10t+12 The particle is at the position x=2 at…

Q: An oil storage tank ruptures at time t =0 and oil leaksfrom the tank at a rate of r(t)  = 100e-0.01t…

A: Given: Oil leaks from the tank at the rate r(t)= 100e-0.01t liters per minute. we have to find how…

Q: The position of a particle at time t is s(t) = 4t^3. Compute the average velocity over the time…

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Q: Solve the initial-value problem for x as a function of t. dx (t – 12t + 35) dt 1, (t > 7, x(9) = 0)…

A: The given initial value problem is as below.

Q: Solve the initial-value problem for a as a function of t . dx (t2 – 11t + 24) = 1, (t > 8, x(9) = 0)…

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Q: Let v(t) = t2 – 10t be the velocity, in ft/sec, of an object at time t, in seconds. a) What is the…

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Q: A particle moves along the X-axis so that at time t>0 its position is given by x(t)= 2t3 +…

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Q: The position of a particle at time t is s(t)=6t3. a.) Compute the average velocity over the time…

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Q: The position of a particle at time t is s(t) = 4t^3. compute the average velocity over the time…

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Q: At time t ≥ 0, the velocity of a body movingalong the horizontal s-axis is v = t2 - 4t + 3. When is…

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Q: Q2) Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where…

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Q: A particle moves along the x- axis so that its position at the time t is given by x(t) = 21 – 9t²…

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Q: A particle moves in a straight line with velocity v(t)=t2 How far does the particle move between…

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Q: A particle moves along the x-axis so that at time t 0 its position is given by a(t) = -t + 4ť² – 4t.…

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