Find T, N, and x for the space curve r(t) = 7ti + (7a cosh (t/a))j, a > 0. T(t) = (Di+ (Di (Type exact answers, using radicals as needed.)

Q: Let y be the curve with vector form r(t) = (1/(t+ 2), sin(sin(sin t)), e-"). a) Determine whether…

A: The parametric curve is r(t)=⟨1t+2, sin( sin( sin t)),e-t⟩. x(t)=1t+2, y(t)=sin( sin( sin t)),…

Q: Evaluate the line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0,…

A: Given: One-form ω=xydx+12ydy and the parametric curve α:0, ln2→ℝ2 defined by α(t)=e2t, e-2t. To…

Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Find an equation of the tangent plane to the given surface at the specified point. f(x, y) = tan xy.…

A: From the partial derivative with respect to x and with respect to y

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A: In given question that is a conservative vector field mean exact integration in which intrgration…

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Q: Find the function f if. Vf-(3a²y + y², a² + 2xy), Vf dr with and without the Fundamental Theorem of…

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Q: 2. Let R(t) = sin 4t î – bcos"(21) j + 2t k. Find the moving %3D trihedral of the curve of R(t) at…

A: Given

Q: Find T, N, and k for the space curve, where t>0. r(t) = (8 cos t+ 8t sin t)i + (8 sin t- 8t cos t)j+…

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Q: 6. Evaluate the line integral g. x²y² dx + xy dy where C consists of the arc of the parabola y = x²…

A: (a) Direct method The given line integral is ∮C x2 y2 dx + xy dy. The curve C consists of    C1 :…

Q: 10. Evaluate the integral cz(z-1) where C is a simple closed curve in the positive direction that…

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Q: Find the area of the surface generated by eY + e -y revolving the curve x = in the interval -In 2…

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Q: Evaluate fpxV47x² + 47y² dA, where D is the shaded region enclosed by the lemniscate curve r? =…

A: To find the value of the double integral         ∫∫Dx47x2+47y2dA where D is the region enclosed by…

Q: To illustrate that the length of a smooth space curve does not depend on the parameterization used…

A: Length of the curve, rt ,  L=∫abrt˙dt ,    a≤t≤b (a)  Consider the parametrisation of the helix,…

Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Assuming that C is the counterclockwise oriented boundary curve of the unit square in the first…

A: It is an simple and easy question on vector calculus  Can be easily solve by use of green's theorem

Q: Find T, N, and k for the space curves r(t) = (cosh t)i - (sinh t)j + tk

A: Let the given space curve is r(t)=(cosh t)i-(sinh t)j+tk   To determine: The values of the unit…

Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: Q1- The divergence of the function f-(rs cos 0)e, in spherical coordinates is......

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Q: Q1- The divergence of the function f= (r cos 0)e, in spherical coordinates is..........

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Q: Let L be the tangent line to the hyperbola xy = 1 at x = a, where a &gt; 0. Show that the area of…

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Q: Find T, N, and x for the space curve r(t) = (6e'cos t) i + (6e'sin t)j+ 4k. T(1) = Di+Oi+k (Type…

A: Given r→t=6etcosti^+6etsintj^+4k^ We have to find the T, N and κ for the given curve. Differentiate…

Q: 2. Let L be the line tangent to the space curve represented by r(t) = (t² – In(t))i+(e²-t – t)j+…

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Q: Q1- The divergence of the function f = (r5 cos 0)e, in spherical coordinates is...

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Q: Evaluate the integral | (3x – 2 y + :)ds where C is the curve, C, and C, as shown. 3- y² + z² 2. 3…

A: Here, Curve C is equivalent to c1+c2. The point of intersections of c1 and c2 is at 0,1,0.

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. p x2y dx,…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Evaluate the line integral (e*y+ 2x) dx + (e* + 1) dy, where C is a smooth curve from the point (0,…

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Q: - Prove that the contour integral – z)dz = -12i where C is the triangle with points 0, 3i and -4…

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Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

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Q: Evaluate F. dr where F = (x – 3y)i + (y – 2r)j and C is the closed curve in the xy plane, x = 2 cos…

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Q: Verify the Green's theorem for the following integral $. sinydx + (x – cosy) dy where curve C is the…

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Q: Consider the closed curve in the xy-plane given by x² + 2x + y* + 4y = 5. dy -(x+1) (a) Show that dx…

A: Given data:   The expression for the given function is x2+2x+y4+4y=5.   (a) Differentiate the above…

Q: Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points…

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Q: Find the area of the Surface generated by revolving the given curve about the - axis while x is over…

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Q: 13. Let F (x, y) = (1(²y²)x, af(x²y? , a(y²) Y) and suppose that C is a smooth curve parametrized…

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Q: B) Evaluate the line integral F-dr, where F (x, y) = x²y³i+ x°y°j and C is the curve r (t) = (t³ –…

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Q: Calculate the integral ∫C(x2+y2)zds, where the curve C is parameterized by r(t)=(sin3t,cos3t,4t),…

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Q: 2. Let R(t) = }sin 4t î – bcos“(21) j + 2t Ř. Find the moving %3D trihedral of the curve of R(t) at…

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Q: Verify the Green's theorem for the following integral O sinydx + (x – cosy)dy where curve C is the…

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Q: Use Green's theorem to evaluate S,(5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: Q1- The divergence of the function f = (r5 cos 0)e, in spherical coordinates is.. .

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Q: Q1- The divergence of the function f (r5 cos 0)e, in spherical coordinates is...

A: The given problem is to find the divergence of the vector function in spherical coordinates.

Q: Use Green's theorem to evaluate the line integral for the curve C given in the figure. [8y dx + 7x…

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Q: Show that the curve r(t) = (ln t)i + (t ln t)j + t k is tangent to the surface xz2 - yz + cos xy = 1…

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Q: Evaluate the unoriented line integral +y² + z²) ds along the parametric curve a : [0, 1] → R³ with…

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Q: Find the area of the surface generated when the curve y=1/4(e2x + e−2x)is rotated about the x-axis…

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Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A: First we have to find partial differentiation with respect to x , y and z of function f such that-

Q: Find a cubic approximation of r(θ) = (θ 2 , eθ , θ) at θ = 0.

A: given rθ=θ2,eθ,θ to find - cubic approximation at θ=0

Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0…

A: Given,

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.