FP Construct unit normal vectors în1 and în2 %D ||F,||

Q: find a unit normal vector UN to the curve y = x at the point p(1,3)?

A: The given curve is y = x3, we can write it as x3 - y = 0 = f(x,y,z), where z = 0

Q: Let N = (p, q, r) be the unit normal vector at the given point. %3D r(t) = (cos t, sin t, t),…

A: Given Data The unit normal vector is N=<p,q,r> The point is (1,0,0) The vector is r(t)=<cos…

Q: Question 2. Consider a p-dimensional response variable j, containing p variables, with n observation…

A: Given- Consider a p-dimensional response variable y→, containing p variables, with n observation…

Q: Are the following vectors linearly independent? ,,

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Q: e) Calculate the interquartile range of x, using R. f) Calculate the 50th percentile of x using R. 2…

A: e) The objective is to calculate the Interquartile range of x. Interquartile range is the difference…

Q: Question 22. 11 E 5D 7 C If x = 9, is AE parallel to BD ? BC DC A. AE is parallel to BD because = -…

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Q: A normal vector to the graph of z = r²y at the point (2, 1, 4) is Select one: (4, 4, 1) О -4, -4, 1)…

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Q: (-5, 4), (0, 4), (5, 2), (10, 1)

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Q: X-d0.0.0.0.0.0.0.0,0,1) Here X[ 1 ] is the number of patients with mutation at Position 1, X[2] is…

A: In this problem, we are given an observation vector X that represents the number of patients with…

Q: Find the state vector that represents the manager's estimate X0 = [        ,      ]

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Q: The normal vector of x+2y-1-0 (0, 2) (2, -1) (1, 2) O (1, -1)

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Q: An autopart is manufactured by a company once a month in lots that vary in size as demand…

A: Solve the following by simple linear regression method to find the answer, the steps is shown below…

Q: Given the following dataset:

A: Given: Let the functional margin = Y i w. X i+ b

Q: Find the norm of a and the unit vector u in the direction of a if -5 -4 1 ||#| = u = || 18 ||

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Q: A study of the relationship between age and various visual functions (such as acuity and depth…

A: given data 2.67,2.58,2.67,3.94,2.42,2.79,3.90,4.18,3.98,4.42,3.45,4.47,2.53,3.62,2.84,3.53,3.10 n =…

Q: Suppose we set αα to 0.05. If you conduct an appropriate tt-test to address the research question,…

A: We have given that two samples, first one is depressed clients of sample size n1 = 9 and second one…

Q: Assume m₁ = [4., 1.5] and m₂ = [1.5, 0.5] represent the mean vectors of pattern class 1 and class 2,…

A: To find the decision boundary between two classes, we need to find the equation of the line that…

Q: -1 -1 3. Find a particular solution of x' = -2 2 x+ 4 -1 -2 et

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Q: A clinical psychologist thinks that depression may affect sleep. She decides to test this idea. She…

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Q: Find the principle unit normal vector to the curve given below at the specified point. Shortcut ok.…

A: Given: Curve equation:  Point: Objective: Find the principle unit normal vector to the curve at the…

Q: find a normal vector to the plane.

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Q: DODH

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Q: The point-normal equation 20x + 1) • y• (2-2) -0 goes through the point P and is normal to n. What…

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Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

Q: Normalize the vectors a ---4:0

A: Here we have to normalize the vectors a and u.

Q: Sketch the curve traced out by the vectorvalued function. Indicate the direction in which the curve…

A: Let F:R2→R, and the parametric equation given is , for t≥0.Since, there are 3 components to F(t),…

Q: n. 1 (0) ---0) 1 2 -1 n1 m1 + P2 — ვ Tვ 2m2 — x3 0 = 0 = 0.

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Q: A study of the relationship between age and various visual functions (such as acuity and depth…

A: Solution-: From the given data we want to calculate (a) ∑xi=?      ∑xi2=? (b) sample variance s2=?…

Q: a) Use Fermat’s little theorem to compute 3302 mod 5, 3302 mod 7, and 3302 mod 11.b) Use your…

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Q: Is the set of the three vectors S linearly independent? Explain why. S = 2

A: From the definition, a set S=v1,v2,v3 is said to be linearly independent if the linear combination…

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: