The displacement from equilibrium of an object in harmonic motions on the end of a string is given by y=1/3cos12t-1/4sin12t where y is meausred in feet and t is the time in seconds. Determine the position and velocity of the object when t=3.14/8 seconds.

Q: Find the equation of the tangent line to the curve (piriform) y^2 =x^3(7-x) at the point (1,√6) a…

A:

Q: Find the equation of the tangent line to the curve y = 5x cos T at the point (T, – 57). The equation…

A: Please refer the attached image for complete solution. THANK YOU.

Q: 5. Determine the equation of the tangent line to (a) r= 2 sin e at = (b) r =1+ cos 0 at 8 =

A:

Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: Given curve is Firstly, we will find value of x and y at t=3pi/4

Q: O Find the equation of the line tangent to the curve at the given value of the parameter. x cost+…

A:

Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0S0< x.…

A: Given :           r=6 cosθ

Q: The exact value of the slope of the tangent line to the graph of the curve r = 9 + 8 cos(e), at e =…

A:

Q: Find the equation of the tangent line to the curve y = 5 sec(x) – 10 cos(x) at the point (T/3,5).…

A:

Q: Let the velocity of a particle be given by v(t) = –sin(t). What is the displacement of the particle…

A: We need to find displacement and total distance.

Q: A particle is moving in such a way that its velocity v is given by the equation v(t) = cost + sin t.…

A: Given : vt = cost + sint

Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26p units along the…

A:

Q: Suppose the position function of a particle is given by r(t)=(√3 sin(t), t-2, √3 cos(t)). If the…

A:

Q: A pole of length L is carried horizontally around a corner where a 3-ft-wide hallway meets a…

A: Given: Pole of length (L): (x+(L-x))

Q: A military radar identified an unknown object flying above Andaman Sea. The Radar Intercept Officer…

A: Given that,The motion of a flying object follows a motion equation,s(t)=sint+6t3s in meter and t in…

Q: A particle travels along a straight line with a velocity v=(12 - 3t®)m/s, where t is in seconds.…

A:

Q: The volume of a right-circular cone of radius r and height h isV = π/3 r2h. Suppose that r = h = 12…

A: Consider the given: Volume,V=π3r2hr=h=12 cmDifferentiate w.r.t. "r",dV=π32rdrh    ⋯⋯11cm increase in…

Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

A:

Q: A military radar identified an unknown object flying above Andaman Sea. The Radar Intercept Officer…

A: Differentiate the distance function, s(t) with respect to t to calculate the velocity function,…

Q: nswer two only: [25] M W Find the equation for tangent to the curve y = x + cos(2x²) at x = 2.

A:

Q: A particle moves along a straight line according to the velocity function v(t)=sen(ωt) cos2(ωt).…

A:

Q: Find the point on the curve r(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13π units along…

A: The smooth curve is rt=12sinti-12cost j+5t k at a distance L of 13π units a curve from point…

Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: A military radar identified an unknown object flying above Andaman Sea. The Radar Intercept Officer…

A: The velocity function is calculated by differentiating the distance function with respect to the…

Q: A one-meter long bar is heated unevenly, with temperature in degrees Celsius at a distance a from…

A:

Q: e cos at the Find the equation of the tangent line to the curve y = point (e?, 0).

A:

Q: The velocity (in meters/sec) of a particle moving along a straight line is given by v ( t ) =2 t^2 +…

A:

Q: Given x= cos0 y = cos 30 (a) find the points on the curve where the tangent is horizontal or…

A:

Q: If an object moves along a line with its position (in meters) after t seconds given by f(t) (1+ sin…

A:

Q: A car is moving at a constant acceleration of 3.6 m/s away from a tree. Atr= 0, the car is 11 m away…

A:

Q: b) Find the point's acceleration at the specified time. s"(2) = ft/sec2 %3D

A: we have been given  s=3t-3t2   , t=2s'(t)=ddt3t-3t2s'(t)=-3t2+6t3now…

Q: Suppose an object moves along a line at 13 m/s for 0sts2 s and at 22 m/s for 2<ts5s. Sketch the…

A:

Q: The following figure shows the velocity, in cm/sec, of a particle moving along a number line.…

A:

Q: Find the equation of the tangent line to the curve y = 3 sec(x) – 6 cos(x) at the point (T/3, 3).…

A: Given : y =3secx - 6cos(x)

Q: The derivative dy for the function %3D (1i) y= cot リーCof V-x

A:

Q: A ping-pong ball is caught in a vertical plexigiass column in which the air flow alternates…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A:

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: To find the slope of the tangent we need to find dy/dx Then find dy/dx at t=pi

Q: Find the length of the curve. x = cos t y = sint 0 <t< 2n

A:

Q: A military radar identified an unknown object flying above Andaman Sea. The Radar Intercept Officer…

A:

Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: Find an equation of the tangent line to the curve at the point corresponding to the given value of…

A:

Q: (a) Find the equation of the tangent line to the curve x = e', y=e %3D at t = 1 without eliminating…

A:

Q: Determine the tangent line to the curve when t=2 x=e^2t sint and y=e^3t

A:

Q: The motion of a cam is defined by the relation @=0.30t(12-t2) where @ is expressed in radians and t…

A: We are given : θ=0.30t(12-t2)=3.6t-0.30t3 Angular Displacement at t=4 : θ(t=4) =0.30(4)(12-16)=-4.8…

Q: (a) Find the slope of the line tangent to the curve y = sin x at the point where x = T/3. (b) Show…

A: (a) we have to  find the slope of the tangent line to the curve y=sin5x at the point where x=π3. as…

Q: x = 6 sin t, y = t +t at t = 0.

A: Let's find.

Q: a) Differentiate implicitly to find for the equation x cos y = x2 y2 +1 dx %3D b) Find the equation…

A:

Q: Find the equation of the tangent line to the curve y = 4 sec(x) – 8 cos(x) at the poin (T/3, 4).…

A:

Q: that cos (x-T) 2/a Find the puints on the curve y= 2x-3x-12.X + 20, where the tangent is parallel to…

A: