A fun ride for children follows the curve with equation y= /2 sin + V2 cos 12 +2, 0sxs 24, where y is the height from the 12 ground in metres and x is the horizontal distance travelled. Express Z sin x) + Jz cos -x | in the form r cos 12 b What is the maximum height of the fun ride? Sketch the graph of the curve y = 2 sin 12 x |+2, 12 + cos 0

Q: Find the lengthof the curve r = a sin² (0/2), 0 0

A:

Q: 6. (d) Sketch the curve described by x = 2 sin t , y = 2 cos t (you can use your calculator). (e)…

A: To sketch the curve x=2sint,y=2cost

Q: Find parametric equations for line that is tangent to the curve x=cost, y=sint, z=t at the point…

A:

Q: . The eight curve x = (1/2) sin 2t, y = sin t, 0 stsa (one loop) y -1

A: Given, xt=12sin(2t)y(t)=sin(t) , 0≤t≤π    The area of R is given by A=12∫xdy-ydxNow on…

Q: Find T, N and B for the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) at the point t = 0 Give your…

A: Given that, r→t=4 cos 5t,  4 sin5t,  5t  at the point   t=0

Q: 4. Find the acute angle between the curves y = sin r and y = cos r (0 < r <) at their point of…

A: We find the point of intersection by setting them equal

Q: Find the points of inflection of the graph of the function. (If an answer does not exist, enter…

A: Find inflection of points and concavity.

Q: Find the horizontal and vertical asymptotes of the curve

A:

Q: A bullet fired from a gun follows the trajectory x = at, y = bt – 16t2 (a, b > 0) Show that the…

A:

Q: Find the length of the curve y In (cos x), 0sxs- 3 The length of the curve is (Type an exact…

A: The length of any curve for x1≤x≤x2 is given by,l(Length)  = ∫x1x21+dydx2  dx   Also use ∫secx dx =…

Q: The curves r¡(t) = (2t, t², t³) and r2(t) = (sin(t), sin(3t), 2t) intersect at the origin. Find…

A: If there are two curves y=f1(x) and y=f2(x) which intersect each other at point (x0, y0).  The angle…

Q: Sketch the solid described by the given inequalities: 0&lt;=r&lt;=2, -pi/2&lt;=theta&lt;=pi/2,…

A: First draw the first two inequality 0&lt;= r &lt;=2 and –pi/2&lt;= theta &lt;= pi/2 in the…

Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

A: topic- area bounded by curves

Q: Q1 Find all the points of intersections of the curves r = 1+cos0 and r=1+sin r-1+(8) r=1+1)

A:

Q: Suppose you start at the point (0,0, 3) and move 10 units along the curve given by 7 (t) = (3…

A:

Q: Find T and N for the curve 7(t) = (3 cos(5t), 3 sin(5t), 2t) at the point t = 0 COS Give your…

A:

Q: Find the arc length of the curve c(t) = (cos(11t), sin(11t), 213/2) on the interval 0 < t < 1.…

A:

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . 4

A: Given that, y = ln(cosx) To find length of curve, we have formula Length of curve = ∫ab1 + [f'(x)]2…

Q: The curves r₁(t) = (5t, t², t3) and r₂(t) = (sin(t), sin(5t), 4t) intersect at the origin. Find…

A: see my solution below

Q: Sketch the graph of two functions g(x) = cos x and h(x) : plane. Choose [a, b] that satisfied |b –…

A: Given function is g(x)=cosx and h(x)=x/2

Q: Find the lengths of the curves x = 8 cos t + 8t sin t, y = 8 sin t - 8t cos t, 0 … t … pi/2

A: The length of the curve of any given function by the formula L=∫t1t2dxdt2+dxdt2dt. Here t1 and t2…

Q: Find all points (if any) of horizontal and vertical tangency to the portlon of the curve shown x-…

A:

Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…

A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…

Q: Find ſo F · dr for F = 8yi – (sin y)j on the curve counterclockwise around the unit circle C…

A:

Q: Show that the curve x = 3 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

A:

Q: Find T, N and B for the curve 7(t) (2 cos(2t), 2 sin(2t), 5t) at the point t = 0 Give your answers…

A:

Q: . The curve with parametric equations x = (1 + 2 sin 0) cos 0, y = (1 + 2 sin 0) sin 0 is called a…

A:

Q: Find the length of the curve y=In (cos x), -≤x≤0. The length of the curve is. (Type an exact…

A:

Q: Find the length of the curve r = 4 – 4 sin 0

A:

Q: A fun ride for children follows the curve with equation Vi in x + 2 +2, 0 sxs 24, where y is the…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: 3IZ 21 C 2 3 3 y

A: With the given information, r(t),x(t),y(t),z(t).... Let us start the solving the problem step by…

Q: An example of cissoid of Diocles is r = sin 0 tan 0 whose graph is below. Show this curve has the…

A:

Q: Find the length of the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) for – 3 < t < 9 Give your answer to…

A: Given: r→t =4cos(5t), 4sin(5t), 5t  for -3≤t≤9

Q: Q8:- Find the intersection points between the given curves. r= cose 1- r= sin0 2- r= 3cos0, r=1+…

A:

Q: ..... The area of the surface generated by revolving the curve x = 1 cos (2t), y = 7+ -sin (2t) on…

A: Follow 2nd and 3rd step.

Q: 2. Eliminate the parameter to find a description of the shape graphed by the para- metric curves…

A:

Q: i) State the domain and range of y = 4 cos-'(3- 2x). %3D (ii) Hence sketch the curve y = 4 cos-(3…

A: Domain and range

Q: 1. Determine the real root of the equation r sin(r) + cos(x) bisection method with 3 decimal places…

A:

Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: Given: x=8cost+8tsinty=8sint-8tcost0≤t≤π2

Q: Find the points on the givern curve where the tangent pairs.) 7= 6 cos(0) horizontal tangent (r, 8)…

A: Consider the given Curve, r=6cosθ Find the points on the given curve where the tangent line is…

Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: Find the distance traveled by a particle with position (x, y) as tvaries in the given time interval.…

A:

Q: Find the cosine of the angle between the curves (cost, -sin(t)/5, sint) and (cos(nt/3), sin(nt/3),…

A:

Q: The curves r1(t) (- 5t, t°, t*) and 72(t) (sin(5t), sin(2t), t) intersect at the origin Find the…

A: Find the thetha

Q: The velocity of a particle moving in the xy plane is given by the parametric equations dx/dt=…

A: The given parametric equations of the particle is dxdt=-2t sin2t and dydt=2t cos2t. Evaluate the…

Q: Show that the curve x = 3 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

A: on solving this we get

Q: jw F(w). 2 - TAN [* - ACOS(WT)] acos Tjw jw F(W) = -2A (₁ - cos (WT)). Tjw jWF(W) = -2A (asin" (WI))…

A:

Q: At what points does the curve 2a cos t - a cos 2t, y = 2a sin t – a sin 2t x = ave vertical or…

A:

Q: TQand TR are secants from Point T to Cirlce A as shown below: s. If mQR = 70° and mSP 34°, what is…

A: Given: To explain the correct of the given statement as follows,