# 3 Let act) (cost, sint a is plane Siht) %3D Decide whether not ? curve

Q: Use the model for projectile motion, assuming there is no air resistance and  g = 32 feet per second…

A: Given Data: The gravitational acceleration is: g = 32 ft/s2 The initial height is: hi = 6 ft The…

Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? + z? = 25 at the point…

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Q: 3) Find the radius of curvature for the parametric curve e-t cost , y = e-t sin t.

A: Given parametric curve is x=e-tcost, y=e-tsint. We know that the Radius of curvature of a parametric…

Q: = 21 which is parallel to the plane Find the equation of tangent plane to the surface x? + 2y? + 3z2…

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Q: Find parametric equations for the line through Po= (3, -1, 1) perpendicular to the plane 3x + 5 y -…

A: Given:  a Point Po =(3, -1, 1)  and a vector perpendicular to the plane is…

Q: Find parametric equations for the lines with the given description.Perpendicular to the xy-plane,…

A: The line is perpendicular to the xy-plane and passes through the origin;

Q: The equation of the tangent line to the parametric equations, x =t +sint, y 4t-cost att 0 is y = -1…

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative…

Q: 7. With an initial velocity of 90 ft/sec and an angle of 20°, a bad golfer strikes a golf ball. (a)…

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Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

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Q: 3) Find the radius of curvature for the parametric curve e-t cost, y = e-t sin t.

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Q: Find parametric equations of the normal line to x2 the surface z + y? 4 at the point (2, 3, 10)

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Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (1,…

A: We have to find the distance between the point 1, 6, 5 and the plane x-y+2z=8.

Q: Q3/ Find the real number such that the line of parametric equations x = t, y = 2 - t, z= 3+t, is ax…

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Q: Sketch the curve x = 3sin?t, y = 4cos?t (0<t <÷) by eliminating the parameter, %3D and indicate the…

A: Introduction: When a function y=fx can be expressed as x≡xt,y≡yt by introducing a new variable t,…

Q: solid that results when R is revolved about the y-axis.

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Q: The parametric equation of the motion of a particle on a plane is given by 3/2. x = te + 2t12; y=t'…

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Q: Find parametric equations of the normal line to x² the surface z = + y? 4 at the point (2, -3, 10)

A: Given curve

Q: Use cylindrical coordinates to evaluate V9-x² r9-x²-y² a² dz dy dx -3 J- 9-x² Jo Do not forget to…

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Q: 1. (a) Parametrize the curve of intersection of the sphere a? + y? + 22 22 + 222 = 1, Try your best…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q5] What is a parametric representation of a curve? What is its advantage?

A: We are entitled to solve only one question at a time so we will answer only the first question.…

Q: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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Q: Saved Match the parametric equations with the corresponding plane curve displayed. x=t-75 ly=? 130…

A: Given : Parametric equations x = t - 75y = t3   To find : Correct graph of the given parametric…

Q: Parametrize the intersection of the surfaces using trigonometric functions. y2 - z? = x - 7, y² + z?…

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Q: Fhd the equation of the tangent plane and normal line to the surface z = 2+y at the point (1, 1,3).

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Q: (a) Find the exact length of the curve (i) r = 1+ sin 0, 0<0< 2ñ, (ii) r= 2(1+ sin 0), 0<0< 27. (b)…

A: If f is continuous and non negative on the interval α≤θ≤β with 0&lt;β−α≤2π. Then  Arc length of…

Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

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Q: The diagram shows part of the curve with parametric equations x = 2 In(r+ 2), y =+21 + 3. (1) Find…

A: The gradient of any curve y is given by its derivative dydx. The given parametric equations of the…

Q: 1. Evaluate the length of the curve defined by the parametric equations x = cost, y=sint, z…

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Q: 4) The lemniscate curve (x² + y²)² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted…

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Q: The two surfaces x2 + y2 + z? = 6 and 2x2 + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…

A: We have to find angle between two tangents - First we will find divergence of function f at point…

Q: Can you help me Graph the curve parametrized by r(t) =⟨1−3t^2,t⟩, −∞<t<∞

A: The given parametric equation is rt=1-3t2, t. Note that one of the coordinate having degree 2 and…

Q: The surface given by z = x² – y? is cut by the plane given by y the point (1, 3, –8). 3x, producing…

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Q: (a) Find equation of the tangent plane and normal line to the sphere x + y +z = 25 at the point…

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: a) Find the are length of the parametric curve x = B(t. sint), y = B(1+ cost), in the range 0 sts,…

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Q: Find the area of the surface generated by revolving the curve about each given axis. X = 4t, y = 8t,…

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Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

Q: 2. Use parametric equations to derive the formula for the lateral surface area of a right circular…

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Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (5,…

A: x - y +2z =4 x - y +2z -4 = 0 compare with equation Ax +By +Cz +D =0 A=1 B=-1 C=2 D = -4 point…

Q: Determine the length of the parametric curve given x = 6 sint, y = 6 cost, ㅠ 0 ≤ t ≤=.

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Q: A cycloid has parametric equations z =t - sint, y = 1 - cost, 0 <t< 2x. Find the slope of the…

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Q: Given the parametric curve. x = 5t2 – 6t + 4 y = t² + 6t – 1 Please find 1) The slope of the curve.…

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Q: Find parametric equations for the semicircle x2 + y2 = a2, y&gt; 0, using as parameter the slope t =…

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Q: 7. Sketch the curve with parametric equations x = e-t , y = e', teR.

A: Topic = Functions

Q: find parametric equations for the line tangent tothe curve of intersection of the surfaces at the…

A: Given surfaces, x2+2y+2z=4     and   y=1f(x,y,z)=x2+2y+2z-4          and   f(x,y,z)=y-1  And point…

Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (1,…

A: Given the point (x,y,z)=(1,2,0) and the plane ax+by+cz+d=0 is given by (x-y+2z-8=0). We need to find…

Q: Plot the parametric curve x=t^3 ; y= sin(t^3); for (t, -2, 2). a) what familiar curve is produced?…

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Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (1,…

A: Plane, x-2y+2z=8 Point A(1,2,4)

Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? +z? = 25 at the point…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Consider the parametric curve C defined by x = x (t) and %3D y = y (t). (a) How do you find the…

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