The distance, s(t), in feet, traveled by a ball rolling down a ramp is given by the function                                s(t) = 5t2, where t is the time, in seconds, after the ball is released. Find the ball’s average velocity from a. t1 = 2 seconds to t2 = 3 seconds. b. t1 = 2 seconds to t2 = 2.5 seconds. c. t1 = 2 seconds to t2 = 2.01 seconds.

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Q: Find the x-coordinate on the graph of f (x) = x ³ – 12 x where the tangent is horizontal. A) 1,-1 B)…

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Q: The distance, s(t), in feet, traveled by a ball rolling down a ramp is given by the function s(t) =…

A: Given the distance in feet travelled be a ball rolling down a ramp is,  S(t) = 4t2 .  Where 't' is…

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A: Given that: s(t)=t3-9t2+18   NOTE: As per our answering guidelines, we can only answer 1 question or…

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Q: Find the derivative of the function. f(t) = (6t + 7)2/3

A: Consider the given function below:

Q: Find the derivative of the function.

A: ddx3x2+4x-8x32Apply the Quotient Rule:  fg'=f '·g-g'·fg2=ddx3x2+4x-8x32-ddxx323x2+4x-8x322Solving,…

Q: If an object is dropped from a 674​-foot-high ​building, its position​ (in feet above the​ ground)…

A: (a) The given function is dt=-16t2+674. Differentiate the function with dt=-16t2+674 by the power…

Q: For the function f (t) = 3t4 – t, the average rate of change in f from t = -1 to t = 3 is %3D…

A: The average rate of change of a function f  on the interval a,b is defined as fb-fab-a. Here,…

Q: Find the derivative of the function. h(t) = t2(3t + 7)3

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Q: The wind-chill index is modeled by the function W = 13.12 +0.6215T – 11.37v0.16 + 0.3965TV0.16 ,…

A: When partial differentiation is done with respect to a variable, then other variables are treated as…

Q: For f(t) = (2x − 3)3, find the equation of the tangent line at (a)  x = 0 (b)  x = 2

A: We have to find tangent line to f(x) at two different points, f(x) is given .at x=2 y=1at x=0 y=-27

Q: d*y 4. Find 5 of the function f (x) = - e dz"

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Q: use the position function s(t) = −4.9t 2 + 250, which gives the height (in meters) of an object that…

A: Velocity is a vector quantity, which is defined as the rate of change of displacement with respect…

Q: Find the second derivative of the function F(t) = 5tsin(r³).

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Q: For the function f(x) = 4x² + 2, the slope of the tangent line at x = 3 is a m = 32 b m = 4 m = 8 d…

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Q: The distance, s(t), in feet, traveled by a ball rolling down a ramp is given by the function…

A: Average velocity: Average velocity of any function s(t) on t1, t2 is ∆s∆t=st2-st1t2-t1 Given that…

Q: find derivative of the function  h(t) = t2(8t + 7)3

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Q: For the pair of functions, find the derivative of the composite function k(t(x)) in terms of one…

A: Obtain the composite function as,

Q: Find the derivative of the function .

A: The given function is  ft=t23-t13+4

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Q: Find the second derivative of the function. g(t) = −8t3 − 5t + 12

A: To find the second derivative of the function gt=-8t3-5t+12

Q: Find the derivative of the function. s(t) = 43 (9t° - 7) s'(t) =| 514

A: S'(t)=?

Q: Find the derivative of function defined as follows. s(t) = 12(2t4 + 5)3/2

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Q: Find the derivative of the function. f(t) = (4t2 − 6t + 7)3⁄2

A: Topic:- derivatives

Q: Find the second derivative of the function.

A: The given function: g(t)=-8t3-5t+12

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Q: Find the derivative of the function. 8t? f(t): V 5t2 + 4t - 1

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Q: Find the derivative of the function. g(t) = (3t2 + 4t − 8)/t3/2

A: The function is gt=3t2+4t-8t3/2.   If a function is of the form, y=fxgx, then the derivative of the…

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A: We have to find the derivative of the function f(t)=9t+223.

Q: The lynx population on a small island is observed to be given by the function P(t) = 120t – 0.4t +…

A: Given that

Q: Find the derivative of the function. f(t) = (3t + 18)2/3 f '(t) = 3V31 + 18

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Q: Assume h(x) = (f(x))3. If f1(0)= −1/2, and f(0) = 8/3, determine an equation of the line tangent to…

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Q: The height, in feet, of a particle from the ground is given by the function s(t) = 1.1 + 19t, where…

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Q: Use the position function  s(t) = −16t2 + 500,  which gives the height (in feet) of an object that…

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Q: I. Find the derivative of the following functions: a. f(r) = 23 + 6x b. h(r) = (3r + 4)2 c. y = Vr3

A: According to company rules, I need to solve first 3 subparts when multiple subparts are posted

Q: Find the derivative of the function C=25(11q^5−14)^8.

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Q: Find the second derivative of the function F(t) = 4tsin(r4).

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Q: The height, in feet, of a particle from the ground is given by the function s(t) 3t2 + 19t, where 0…

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Q: From the previous number, compute for the derivative value of the maximum magnitude. A. 20.4861 C.…

A: Find directional derivativeϕ=z sech-1y tan-1ln x in the direction of dx=2dy=-3dz at point e3, 0.5, 4…

Q: Find the derivative of the following function: h(t) 10t3 – 4t +7

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Q: Find the derivative of the function. t2 (a) F(æ) = |7 1+t3

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Q: Find the derivative of the function. g'(t) = g(t) = (8t + 8)² (8t² – 8)−3 -

A: We need to find derivative of given function.

Q: The distance, s, of a moving body from a fixed point is given as 24ei. Find the velocity, v, of the…

A: We will find out the required solution.