The displacement of a particle on a vibrating string is given by the equation s(t) = 13 + sin(6πt), where s is measured in centimeters and t in seconds. Find the velocity of the particle after t seconds. v(t) =

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A: It is given that, The plane contains the point 8,4,-8 and the lines x=-4=6t, y=6+t and z=-5+4t.…

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Q: 7. If f(3) = 15, f' is continuous, and f f'(x) dx = 27, what is the value of f(8)?

A: We have given a continous function f' f3=15 ∫38f'x=27 As,  ∫f'x dx=fx ∫38f'x=fx38=f8-f3 So,…

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Q: Problem #1: Evaluate the following integral, Problem #1: (x - 5y) (x - 5y) dx - 2y² dy where C is…

A: Ans=444.5 For detail go through the solution...I have solved in detail

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Q: Write the equation of the line passing through (-7,-6) and (1,1) in the slope intercept form

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Q: ) If g(x) = x³, then lim x-2 g(x) x - 2 - 12

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Q: 10) Consider the following two functions p(t) = and 7e-2)-7 t-2 P: R R if 0 2 q: R→R q(t) =…

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Q: Given Cost and Price​ (demand) functions C(q)=110q+40000 and p(q)=−2.3q+950​, what is the marginal…

A: Given Cost and price function:- Cq=110q+40,000pq=-2.3q+950

Q: The plane containing the point (3,7,4) and parallel to the plane 2x - 3y + z = 8 has equation…

A: Equation of a plane parallel to the plane ax+by+cz+d=0 is given by ax+by+cz+k=0.

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A: To find the extreme values of fx, y=xy subject to the constraint  x2+y2-20=0.

Q: The percent of concentration of a certain drug in the bloodstream x hours after the drug is…

A: Given function k( x ) = 3xx2 + 4

Q: Find the distance from the point (-4,-6,4) to the line a(t) = ( – 5, 1, − 3)t + (− 7, — 4, 7) FORCYY

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Q: Find [." ["v y arctan (1) dydr. dydx. Hint: Use integration by parts.

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Q: 4. √e³x - e²x dx = 3 A. ² (ex - 1)² + C < B 3 B. (e³x - e²x) + C 2|32|3 C. 2/3 3ex - 1 √2 3 D. ²/7…

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Q: The following table records some values of f and its derivative. 1 1 2 3 4 5 6 2 0 1 3645 4-2 1 531…

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Q: x(t) Find the point at which the line y(t) z(t) = = = 4 - 8t -4+ 5t intersects the yz plane. 6 + 2t

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Q: 10. (9x2 + y-1)-(4y - x) y' = 0, y(1) = 0

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=6ey-3ye* Select…

A: The function is given as , fx,y=6ey-3yex find all local maxima , local minima and saddle points.

Q: Find the Taylor series of f(x) = Choose the Taylor series. 1 1 X 1 X 1 - x 1-x = = = (-1)"+1 Σ(1)",…

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Q: Three runners compete in a 100-meter hurdle race. The graph depicts the distance run as a function…

A: Observe the given graph and answer each part.