For numbers 7 and 8. Let v(t) =t2 – 2t – 5 be the velocity function for a particle moving along a straight line. Here, velocity is measured in meters per second.

Q: Compute the values of dy and Ay for the function y= e4z + 5z given z = 0 and Az = dz = 0.02.

A: Given x = 0, dx = ∆x = 0.02            (1) Here y = f(x) = e4x+5x

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

Q: The position function of a particle is giyen by s(t) = (t – 1)²(t – 3) , where t is measured is…

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Q: For numbers 7 and 8. Let v(t) =t? – 2t – 5 be the velocity function for a particle moving along a…

A: Let's find.

Q: A particle of mass m moves through a fluid, subject to a resistance R that is a function of the…

A: Hi. You have posted multiple questions in a single request. We will only solve the first one. Post…

Q: Suppose that a particle moves along a straight line with a velocity v(t) = 4– 2t, where t is in the…

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Q: The gradient of the curve y =x+ 3x + 4x at the point where x =1 ise A В 4 13 D E 16

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Q: Given the function y(t) with y(0) = 1, then False True L (y² + ²) = SY(s) - 1 + y(s)

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Q: #26

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Q: T(E) = N= T'(4) Evoluate (t) NG) for t=L,

A: First we find r'(t) then put t=1

Q: Find s(t), where s(t) represents the position function and v(t) represents the velocity function.…

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Q: Find s(t), where s(t) represents the position function, v(t) represents the velocity function, and…

A: Given a(t)=-30t+8, with v(0)=7 and s(0)=6. where s(t) represent position function, v(t) represent…

Q: Determine dz for z = f(x, y) = e^(x^2+y^2) if x changes from 1 to 1.02 and y changes from 2 to 2.1.

A: use formula :-    dz = fx(x,y)dx + fy(x,y)dy

Q: If v(t) is the velocity of a moving object in feet per minute, then what do the following represent"…

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: 4. The position of an fictitious particle moving in a straight line, in metres, is described by the…

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Q: For the following position functions y=s(t), an object is moving along a straight line, where tt is…

A: 1. The formula for average velocity is Vavg=st2-st1t2-t1 We have s(t) = 2t3 + 3…

Q: Find s(t), where s(t) represents the position function, v(t) represents the velocity function, and…

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Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

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Q: Suppose an object moves along the x-axis so that its position at time t is x = −t +t3/6 (a) Find…

A: Note: There are many subparts in the questions so I will answer the first three questions and other…

Q: - The position of an object moving on a line is given by s(t) = 6t2 – t°, t > 0,

A: Solve

Q: For the linear function y = f(x) = 5x+8:  Find df^−1/dy at y = f(10). (f^−1)'(f(10))=

A: Giveny = f(x) = 5x+8Replace x=f-1(y)Nowf(f-1(y))=5f-1(y)+8y-8=5f-1(y)f-1(y)=y-85

Q: The position function of an object is given by s(t) = -t + 2t. For t > 0 and s(t) = 0m, the velocity…

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Q: For a t-curve with df = 11, find the t-value to 10: O A. 1.280 ОВ. 1.363 O C. 2.718 O D. 1.372

A: Given Degrees of freedom (df)=11

Q: Suppose that a particle moves along a straight line with velocity v(t) = 15 – 1t, where 0 <t < 11.5…

A: Given : v(t) = 15 - t  0≤ t ≤ 11.5

Q: The velocity of an object moving in a straight line is given (in m/s) by v(t) = 2t – 3. Find the…

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Q: or~r(t) =⟨3t−1,7t+ 2,t2⟩, t0= 1 find an equation o

A: Given: The parametric curve via position vector, r(t)=&lt;3t-1, 7t+2, t2&gt;. We need to find the…

Q: The value of b makes the line y = 2x +b be tangent to the function f (x) = x² is O -1 none О 1 O 2

A: Tangent line related problem......

Q: Find the differential of the function. z = 7t − 7/t2

A: zt=7t-7t2

Q: Suppose the position of an object moving in a straight line is given by the specified function. Find…

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Q: For a t-curve with df = 11, find the t-value to 10: O A. 1.280 В. 2.718 O C. 1.363 O D. 1.372

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Q: A ball rolls down an inclined plane such that the distance (in centimeters) that it rolls in t…

A: Differentiate the function s(t)=2t3+3t2+4 to find the velocity function.…

Q: Given the function(x) = x3+ 1, find the ∆y, dy, ∆y-dy

A: f(x)=x3+1

Q: For the linear function Y 3: df a. Find at a = 10. dr f'( – 10) : o. Find a formula for a = f'(y). f…

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Q: The velocity, v of a body as a function of time, t is given as v(t) = 3e 2t + 2, where t is in…

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Q: If y1=2x+4 and y2=x^2+C, find the value of C such that y2 is tangent to y1. O 5 O 6 O 7 4.

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Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: The displacement (in meters) of a particle moving in a straight line is given by s = t2 – 3t + 10…

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Q: Find the linear approximation at x=0 to √17−x. Write your answer in the form y=Ax+B.

A: we have f(x)=17-xDifferentiating both side w.r.t "x"f'(x)=-1217-x-12f'(x)=-1217-xput x=0f'(0)=-1217…

Q: The position function of a particle is given by s(t)=t^3−4t^2−8t, t≥0 where s is measured in meters…

A: To find the velocity function from the position function, we have to differentiate position function…

Q: The position of an object moving along a straight path is given by s(t) = 1.8t2 – 3.1t + 6.7. Find…

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Q: For the function f(a, y) = wy - 2, we have f(2, -1) = -6. Use a linear approximation to estimate…

A: Solution of given problem is given as:

Q: For the position function of a ball given by s (t) = 64 – 16(t – 1), find the most simplified…

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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: If y1=2x+4 and y2 =x^2+C, find the value of C such that y2 is tangent to y1

A: Given: y1=2x+4    and    y2 =x²+C   To find :the value of C such that y2 is tangent to y1

Q: Find the length L of the curve R(t) = 4ť²i + t° j+ 4k over the interval [3, 6]. L

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Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: The velocity, v of a body as a function of time, t is given as v(t) = 5e4+4, where t is in seconds,…

A: Since, we have been given that v(t)=5e-2t+4-(i), where t is in secondsand v is in m/s.Our Aim is to…