The position of an object moving along a line is given by the function s(t) = -17t + 153t. Find the average velocity of the object over the following intervals. Ca) [1, 7] c) [1, 5] (b) [1, 6] (d) [1, 1+ h] where h>0 is any real number.

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t…

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Q: Calculate the length of the curve F (t) = (2t-1, t + 1) with t ∈ [1,2].

A: Given that  the curve F (t) = (2t-1, t + 1) with t ∈ [1,2]. To Calculate the length of the curve in…

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Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

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Q: Given that the line y= 2x +c is a tangent to the curve y = kx, where c and k are positive constants…

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Q: For the position function, s(t)=-16t2+103t​, complete the following table with the appropriate…

A: Consider the position function, s(t) = 16t2+103t.

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A: We have to find the instantaneous velocity of y at specified value x at x=2

Q: The position of an object moving vertically along a line is given by the function ​s(t) = -4.9t2 +…

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A: Given,

Q: Suppose that a particle moves along a straight line with velocity defined by v(t) = (10t(4 − t))/((t…

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Q: Can you please solve these two sub problems and show all of the steps and say the correct letter

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 5t…

A: Given:The velocity function of the particle is v(t) = 5t-8.

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A: To find: The instantaneous velocity at t=2. Given: The acceleration of particle is a=12t2-24t+8.…

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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

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A: Given

Q: The position of an object moving vertically along a line is given by the function s(t) = - 4.9t +27t…

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Q: The linear approximation at x and where B is:

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Q: The position of an object moving vertically along a line is given by the function s(t) = - 4.9t +…

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Q: s(t)%3D512 +t3 :-

A: Given information: st=5t2+t3 Find the velocity at -2.

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Q: Find f(x) if y = f(x) satisfies %3D dy 42ya3 %3D dæ and the y-intercept of the curve y = f(x) is 4.…

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Q: The displacement (in meters) of a particle moving in a straight line is given by s = t2 – 5t + 15,…

A: Given: s=t2-5t+15, where t is measured in seconds

Q: Let f(x) = 2x³ – 9x² – 24x + 19 A. Differentiate f. B. Determine the values of r , if any, at which…

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Q: Find the equation of the tangent plane to z = e + x + x³ + 9 at the point (2, 0, 20). z =

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Q: Find the derivative of the function f(x, y) 5x2-3y at (8,4) in the direction of A = 3 i-4j O 412 492…

A: First of all we will find gradient, then we will find the directional derivative

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A: z = f(x,y) f(x, y,) - z = 0 Tangent at (0, 0) with direction <a, 0, c>

Q: given the position function for an object in motion is s(t)=2t2+4t-1 what is the average velocity on…

A: Definition used:The average velocity of an object with position function f(t) over an interval [a,…

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Q: Find the displacement of an object on the interval 0 ≤ t ≤ 6 if its velocity is v (t) = 4t -√√t

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Q: Find the absolute maxima and minima of the function f (x,y)=2x²-4x+y²-4y+1 on the closed triangular…

A: Given:The given function is f(x,y)=2x2-4x+y2-4y+1 on closed triangular region bounded…

Q: The position function of a particle moving along the x−axis is given by x(t)=t3−4t2+5t−2, t≥0. Find…

A: We find the velocity by finding the first derivative of x(t)

Q: Suppose that a particle moves along a straight line with velocity defined by v(t) = 10t(4 − t) (t +…

A: The given data isVt=10t4-tt+1t-7m/s.To find:The distance travelled by particle over interval t∈0,6.

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Q: Find the interval on which the curve 1 dt 4+t+ 2t2 is concave upward.

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Q: Consider the function y defined implicitly by 3(x2 + y2)? = 100xy. Use the linear approximation at…

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Q: The tangent line to the curve y=vx-5 * for x=16 is a. y=1/8 (x+16). O b. y-4=1/6 (x-16). O c.…

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Q: A particle is moving in a straight line with the velocity v(t) =1-t,0<t< 3. Compute the distance…

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Q: Let v(t) = 3t – 5 be the velocity function for a particle moving along a straight line. Here,…

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Q: Q1) Find the tangent y = vx² – x + 7 at x = 2.

A: The detailed solution is as follows below:

Q: Find the equation of the tangent plane to z = e + x + x² + 4 at the point (3, 0, 17).

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Q: 2- Use Lagrange interpolation formula to determine the relation between the velocity of the rocket…

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Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

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