Given the velocity v = ds and the initial position of a body moving along a coordinate line, find the body's position at time t. dt v = 9.8t + 8, s(0) = 15 s(t) =

Q: The position of a moving particle is given by s(t) = t2 – 7t + 4 on the interval 0 <t< 4, where 's'…

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Q: The velocity in m&gt;s of an object moving alonga line over the time interval [0, 6] is v(t) = t2 +…

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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 - 2t +…

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Q: Given that x and y are functions of time, find the indicated rate of change dx/dt, when x = 2, y =…

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Q: a) What is the particle's position at time 2? b) What is the particle’s displacement from t= 1 to…

A: (a) The function representing the position is  X(t)=t3-15t2+48t. To find the position of the…

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: 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: If a ball is thrown straight up into the air with an initial velocity of 60 ft/s, its height in fe…

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Q: A mining expert estimates that the production growth rate of copper overtime, or ,is given by dt' dy…

A: By using integration.

Q: With what initial velocity v0 must we fire a rocket so it attains a maximum height r above the…

A: We will use the maximum height formula Where u=initial velocity. g=gravity H_max= maximum height

Q: Given the velocity and initial position of a body moving along a coordinate line at time t, find the…

A: See attached file for a step by step explanation.

Q: The position of a moving particle is given by s(t) = 2t2 – 18t on 2 <t< 9 where 's' is in meters and…

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Q: t +t dt

A: Antiderivative: Integration is the inverse process of differentiation.  The operation of finding the…

Q: The position of a particle at time t (s) is s(t) = t2 + 1 m. Compute its average velocity over [2,…

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Q: Given the acceleration a=d^2s/dt^ 2​, initial​ velocity, and initial position of a body moving on a…

A: Given :- a=-81sin9t, v(0)=9,  s(0)=-7 Here, a is accelerationdvdt, v is velocity dsdt and s is…

Q: dv dt    = −kv2 An object moving through the water has an initial velocity of 40 m/s. Two seconds…

A: As the given differential equation is: dvdt=-kv2 Given conditions are:  t=0 , v=40 mst=2s, v=30 ms…

Q: A parachutist of mass m falls from rest in the Earth's gravitational field and is subjected to mg…

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Q: Suppose an object in motion has the given acceleration function. a(t) = 2t m/s? Furthermore,…

A: To determine the velocity of the object.

Q: Two particles have positions at time t given by s =4t-t^2 and s=5^2-t^3. Find the velocities v1 and…

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Q: A particle is moving such that its position after t hours is s(t) =- -measured in meter. 4t +1 Find…

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Q: If the position of a particle is represented by x(t) = -t2 + 1, what is its instantaneous velocity…

A: We are given that the position of a particle is represented by x(t)=-t2+1. Now, we need to find its…

Q: The barometric pressure p (in inches of mercury) at an altitude x miles above sea level satisfies…

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Q: b) The mass (in kg) of a product from a chemical reaction is denoted by 'y'. The dy rate at which…

A: b Separate the terms of both the variables Then let 1+y2=z2ydy=dzand 1+t2=u22tdt=2udu

Q: a. Water is flowing into a conical tank at a constant rate of 3 cubic meters per second. The cone…

A: The answer is given by using volume formula of cone. The answer is given as follows:

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: 1. The position of a particle at time t is given by s(t) = t³ – t2. Using a table, estimate the…

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Q: If f(t)=2t+sin(t) describes the length of an oscillating spring in m/s, what is the instantaneous…

A: Solution is written in below steps.

Q: Find an equation for the instantaneous velocity v(t) if the height of an object is defined as h(t)…

A: To find: The instantaneous velocity at any point in time. Given: The height of an object is .…

Q: A particle moves along the x-axis so that at time t >0 its position is given by x (t) =t² – 10t +…

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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: If s(t) is the position on the x-axis of a particle at time t, then the quantitys(t + h)−s(t) / h…

A: If s(t) is the position on the x-axis of a particle at time t,

Q: An object with an initial velocity of 40 m/s undergoes an acceleration of a(t) = 12t – 10 m/s“, t…

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Q: Find the position of the particle at time t=4. Is the particle moving toward the origin or away from…

A: If the velocity function is given then by integration we will calculate the position of the particle…

Q: What is the position at time t of a car that is accelerating at a rate of 5 meters per second…

A: To determine the position of the car from the given data. (note that s =20 when t=2, not as given)

Q: A particle moves on the 0x axis with acceleration proportional to velocity. Assuming that v(0) = 3,…

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Q: Given the velocity and initial position of a body moving along a coordinate line at time t, find the…

A: Given velocity function  v = -6t + 5

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

A: Given: v(t)=t2ln(t+2)we know that acceleration of particle is differentiation of velocity of…

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 3…

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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: Q 10 Show that for motion in a straight line with constant acceleration a, initial velocity vo , and…

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Q: 1. A particle moves along the x-axis according to the equation x=2r+3F, where x is in m and is in…

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Q: If the distance y from the origin at time t is given by y = -16t² + 3000t + 50,000, find the initial…

A: Given: The distance y from the origin at time t is given by  y = -16t2+3000t+50,000 To find: The…

Q: The acceleration, a, of a particle is given by a = 5- 6t Given that the initial displacement at t=0…

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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: The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a…

A: Height is given by ht=3 sin 2πt→1instantaneous velocity=dhdt⇒Differentiate eqn 1 , w.r.t 't' , we…

Q: The position of a moving particle is given by s(t) =t - 3t + 6 on the interval 0<t<6, where 's' is…

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Q: A spring is stretched 12 inches by a 24-pound weight. If the weight is pulled 10 inches below the…

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Q: the given velocity v(t) = e2ti– sin tk and r(0) = (1,2,0) to find the position at time t = 1.

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.