Q3: A cubic Bezier curve given by the following control points: X= [5 x1 x2 20]; Y=[5 Yı Y2 5].Determine the missing control points knowing that the tangent vector at (t=0.5) T(0.5) = (15,0) & P(0.7)= (17,7.4)

Q: 1. Calculate the moment of inertia about x-axis of the first quadrant portion of the curve: y = 4-…

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Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 21, (1, 4,…

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0).…

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Q: Find thee orthogonal trajection of the one-parameter family of curve ex +e-y =c

A: ex+e-y=c

Q: Find an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: 4. Find an equation of the tangent plane to the surface z = xy+8 at the point (1,1,-10) xy-2x

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Q: e-param

A: Here we have,  ex+e-y=c ................(1)  differentiate with respect to x

Q: Find the equation of the tangent plane to z=e^y+x+x^2+10 at the point (2,0,17).

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Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

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Q: find a parametrization c(t) of the curve satisfying the given condition.  y = x 2, c(0) = (3, 9)

A: The given function is y=x2 and c(0) =(3,9) Let x(0) =3 and y(0)= 9 Take x =t +x(0) Thus, x = t+3

Q: Find an equation of the tangent plane at P = (0, 3, – 1) to the sur- face with equation ze* + ez+1 =…

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Q: 4. Find the equation of the tangent plane to the surface Z = = 5tan(x) – sin(3y) at the point (xoyo)…

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Q: (a) A beam is fixed at its left end x = 0 but is simply sup- ported at the other end x = L. Show…

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Q: YouTrylt 4 Consider the path of a particle given by tangential and normal components of acceleration…

A: The position vector of the particle is given by  r(t) = 2t2, t3, -1

Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

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Q: Find an equation of the tangent plane to the surface at the given point z= 5x - xy3+y2,     (1,1,5)

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Q: find a parametrization c(t) of the curve satisfying the given condition. y = 3x − 4, c(0) = (2, 2)

A: It is given that,

Q: At time t, the position of an ant moving in the xy-plane is given by parametric functions…

A: Given parametric functions are: dxdt=3t+2dydt=t2-4

Q: Find an equation of the tangent plane to the surface at the given point.   z= y/1+6x…

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Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

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Q: find a parametrization c(t) of the curve satisfying the given condition.  y = 3x − 4, c(3) = (2, 2)

A: To find the parametrization

Q: 3. Find an equation of the tangent plane to the paraboloid defined by z= 5x +4y? at the point…

A: The given equation is; z=5x2+4y2 at the point (-1,1,9).

Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

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Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: Find an equation of the tangent plane to the surface at the given point in the figure below.

A: Consider the given:…

Q: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

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Q: The parametric equations of a curve are given by x = In (VE +1) and Vt + y = cosh-(2t). X = dy when…

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Q: find a parametrization c(t) of the curve satisfying the given condition. y = x2, c(0) = (3, 9)

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Q: Find the tangential and normal components of acceleration at the given time t for the space curve…

A: Brief explanation of the answer has been provided in the file attached below. If you have any doubts…

Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: Find the length of parametrized curve given by x(t)=−6t^2−6t,y(t)=−4t^3−6t^2 where t goes from 0…

A: Given information:  The parametric equations are x(t)=−6t2−6t,y(t)=−4t3−6t2 over the interval .0≤t≤1…

Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

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Q: If the equation of the tangent plane to x2+y²-83z2=0 at (1,1,/2/83) is x+ay+Bz+y=0, then a+ß+y=

A:

Q: Find the length of parametrized curve given by x(t)=12t^2−12t, y(t)=−4t^3+6t^2+9t where t goes…

A: Let us consider the parametrized curve x(t) and y(t)  The length of the curve is obtained as…

Q: 9. Find an equation for the tangent plane and the normal line to the surface xy + yz + zx = 5 at the…

A: f(x,y,z)=xy+yz+zx-5=0,  at  (1,2,1)now we differentiate above equation with respect to x,y,z…

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: vember 12, 20Z1 m # 3 Find an equation of the tangent plane to the face at the given point. f (x,y)…

A: Solve the given problem.

Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

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Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

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Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

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Q: Consider the curve in space 7 (t) = (te", vt, v2t) (1) Find an equation of the tangent line at t = 1…

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Q: a. Find the equation of osculating plane to Z1 at t=0

A: A(0) = &lt; -2, 5, 4&gt;     ---(1)  B(t) = &lt; 3/5 cos t , 3/5 sin t , 4/5 &gt;    =&gt; B(0)  =…

Q: Find the equation of the tangent plane to z = e² + y+ y*+3 at the point (0, 5, 634).

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Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: Show that the Bézier curve with control points Po = (1, 4), P = (3, 12), P, = (6, 15), P3 = (7, 4)…

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Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx + x²dy by the curve y y = x2.

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Q: 1. Find the equations of the normal and osculating planes of the curve x Int, y 2t, z = t2 at the…

A: Equation of the plane :  r→.n^ =a→.n^ ; where 'r→' is the position vector and 'a→' is the given…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.