The circles r (V3/2, 7/3). Show that their tangents are perpendicular there. V3 cos 0 and r = sin 0 intersect at the point

Q: The curves T1(t) = (2t, t“, – 4t) and T2(t) = (sin(5t), sin(t), t) intersect at the origin. Find the…

A: Given that  The curves R1 and R2  Intersect at origin  To Find the angle between the curve

Q: Consider the following. X = sin y = os(플e), -π sθ<π (a) Eliminate the parameter to find a Cartesian…

A: As we know that the trigonometric identities:- cos2(θ)+sin2θ=1

Q: Find the area between the two curves in the following figure: r=2a+a cos 20 r=sin 26 For a = 16…

A:

Q: If f(x) = 3x^2/3 − 10, find the arc length of the graph of f from the point A(8, 2) to B(27, 17).

A:

Q: Show that the curves r = a sin 0 and r = a cos 0 intersect at right angles.

A:

Q: Find the length of the following two-dimensional curve. r(t) = (cos t, sin ), for 0sts 6

A:

Q: The slope of the tangent line to the graph of f(z) COS at a is Select one: O a. 00 2 Ob. 2

A: we hav eto find the slope of the tangent line of the given graph at a=π/2

Q: Find the length of the following two-dimensional curve. r(t) = (cos t, sin , for 0sts5

A:

Q: Which of the following is an arc length parametrization of a circleof radius 4 centered at the…

A: First find the derivative of r(t). Differentiating r(t) with respect to t, we have…

Q: In the figure, QS= 5, RT = 12, and RT is tangent to radius QR with the point of tangency at R. Find…

A: In the given question we have to find the length of QT in the given figure. In the given question we…

Q: What curves are represented by the following? Sketch them. [cos t, sin 2t, 0]

A: To Sketch: The curves represented by the parametric form [cos t, sin2t, 0].

Q: the length of the curve r = V1+ cos 20 for – -sos.

A: In this question, the length of the curve is to be determined. Length of Curve The length of the…

Q: Find the moving trihedral of the curve 7(t) at the indicated value: 7(t) = cos? t î + sin? t ĵ + 1…

A:

Q: Assume that the two points (x1 y1) and (x2.y2) lie on the graph of the straight line y = mx + b. Use…

A:

Q: The curves r1(t) = (5t, tº, – 4t³) and T2(t) = (sin(t), sin(3t), t – n) intersect at the origin.…

A:

Q: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

A: Show that for all values of θ and φ, the point (a sinφcosθ, a sinφsinθ, a cosφ) lies on the sphere…

Q: 2. KS is tangent to the circle at T. Secant KR contains P, the center of the circle. PR and PT are…

A: Firstly draw a circle with center P Now draw a tangent KS at point T

Q: Find the length of the following curve at the given distance. Rie). cos'e ?a sin? t } Cos t i 2

A: Given curve is R→t=cos3ti^+sin3tj^ where 0≤t≤π2. We have to find the length of the given curve at…

Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

A:

Q: Find the length of the following three-dimensional curve. r(t) = (cos t, t, sin t), for 0sts8 L3D…

A:

Q: Prove that the curve y:(-,) → R³ is regular with factor H and determine whether the image y (t) = (2…

A: To determine : the      included in a plane in   or not. Here,…

Q: Find the length of the following two-dimensional curve. r(t): = (cos t, sin t) , for 0stsT The…

A: The formula for finding the length of the curve is explained in step 2 with a general observation…

Q: Find the length of one arch of the cycloid 2(t – sin(t)), y = 2(1 – cos(t). х

A:

Q: In the following sketch, AE and BF are tangents to the circle at A and B respectively. AE || CD and…

A:

Q: Given the cardioid r= 3(1+cosθ) 0 ≤ θ ≤ 2π Determine in wich points the cardiod has vertical…

A: Differentiate the equations r=31+cosθ and x=rcosθ with respect to θ, to find drdθ and dxdθ.…

Q: r = 2 cos 0,0 <o <n. 2 L = S°. dr r2 + de de.

A: Use the formula given to find length of curve.

Q: In the figure, QS = 10, RT = 24, and RT Is tangent to radius QR with the point of tangency at R.Find…

A:

Q: 2. AD is tangent to circle E at A. BD is a secant intersecting the circle at F and B. a. Find AD if…

A:

Q: Find the length of the following two-dimensional curve. π 3 r(t) = (3 cos ³t, 3 sin ³t), for Osts- 4

A:

Q: Let C be the curve parameterized by Y: [0, b] R³, y(s) = (12 cos(s²), 12 sin(s), 9 s²). Find b>0…

A: The given problem is to find the value of b for which the given length of curve of the given…

Q: Find the length of the following two-dimensional curve. r(t) = (2 cos t,2 sin t), for 0stsT

A:

Q: Find the length of the curve. r(t) = (9t, 3 cos(t), 3 sin(t)), -5 sts 5

A: To determine the length of the curve.

Q: Sketch the following curves and find the points of intersection of the pairs of curves. a) r=…

A:

Q: Find the equation of the osculating, normal, and rectifying planes for a (t) ( cos t, – sin t, cos…

A:

Q: PQR is an isosceles triangle with PQ = PR. PQ is a tangent to the circle at S. S is the midpoint of…

A:

Q: Find the length of the curve 7(t) = (ei cos(), ei sin(÷), e) n(4),e¿): for 0 <t < 5. CoS

A:

Q: 1. Draw the curve r² = 2a? cos 20, a > 0 and calculate the area enclosed by this curv

A: This question is about application of integration in polar coordinates

Q: In the diagram below the two circles have radius 2 and centers D and G, DH is tangent to C(G, 2) at…

A:

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: To use the geometry we will change the polar equation into the cartesian equation first.  For that,…

Q: Which one of the following points lies on the curver = sin 0 – 5. %3D TT o (-5, n) o (5, 0) (5, 2)

A: Put all points on curve, point which satisfy the equation , lie on curve.

Q: Find the length of the curve over the given interval: r=3acos(theta) Interval: [-pi/6,pi/6]

A:

Q: KS is tangent to the circle at T. secant KR contains P, the center of the circle. PR and PT are…

A: Consider the given information. Let's draw the graph step by step given as KS is tangent to the…

Q: Find the angle of intersection of the following curves r=a(1+sinθ) and r=a(1-sinθ).

A:

Q: (a) Evaluate sin 2z dz, 3z -71 where C is an anticlockwise unit circle centred at the origin. 4.

A:

Q: Consider the following. x = sin(0.5θ),    y = cos (0.5θ),    −π ≤ θ ≤ π (a) Eliminate the parameter…

A:

Q: Consider the following. x = sin coso), -n s 0 sa co). (a) Eliminate the parameter to find a…

A: Our objective to find the cartesian equation of the curve.

Q: Find the length of the following two-dimensional curve. r(t) = (5 cos t, 5 sin ), for 0sts

A: Recall: Length of the Parametric form :L=∫t=at=bx'(t)2+y'(t)2 dt

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: Recall:  L=∫abr(θ)2+r'(θ)2dθ We have, r=7sinθ+2cosθ, a=0, b=π

Q: The parametric equations x = 4 - 5 sin 3t and y = 3 + 5 cos 3t for  0 ≤ t ≤ π/2  represent a curve…

A:

Q: Find the tangent of ZH. J 4 H. 3-/6 Write your answer as an integer or as a decimal rounded to the…

A: Given triangle HJI