...,N, becomes Y = a, + a,X. Q6. (a) If the least square line of points (xţ, Y1), i = 1,2, ... .. Prove that the constant ao and a, will be (ΣΥΣΧ?)- Σχ)/ΣΧΥ) ao NEX2 – (EX)² and ΝΣΧΥ-Σ Χ) (Σ) NEX² – (EX)² (b) Develop the relationship between correlation coefficient and regression coefficient. Mention the applications of correlation and regression. (c) What is rank correlation? How to rank data? Rank and find the rank correlation for the following data of English and Math marks. English (Marks) Math (Marks) 14 56 66 75 70 10 45 40 4 71 60 61 65 51 64 56 58 59

Q: (6) Let -1 3 1 y = 2 and uj = -1 u2 -1 -2 Find the closest point to y in span{u1,u2}. What is the…

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Q: x+2 What is the equation of the normal line of y = at the point x = 1? 2x+1

A: Let us consider function y=f(x) The normal line of function y=f(x) at point x0 is given by formulae:…

Q: Find the x-intercept of the line x+3y-5=0 as a point O a. (0,5) O b. (5,0) O c. None O d. (0,5/3)

A: x intercept can be obtained by putting y=0 in the given equation.

Q: 4 TA 2 -6 -4 -2 2/ 4 6. -2 -4

A: We can find the coordinate of the image of B as below.

Q: Find eqation of line through the point (4,2,1) and (0,4,2)

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Q: Consider a function of 2 variable f(x, y) = 2x³y² – 5x²y* + 3x³ – 4y³ af and Əx af Find ду

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Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

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Q: Show that there are no points (x, y, z) satisfying 2x - 3y + z - 6 = 0 and lying on the line v = (8,…

A: Given line v is: v=8,-8,-4+t(1,1,1)  =(8+t,-8+t,-4+t) Therefore, if (x,y,z) lies on the line v, then…

Q: Which 2 points are on the line (x,y) = (3,7) + k(-1,2), k E R Select one: (-1, 2), (3, 7) (3,7), (2,…

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Q: Find the equation of a line parallel to 2x+y-3-0 passing through (-2, 3). 2y + x + 1 = 0 none of…

A: As per guidelines i can only solve the first question in multiple questions.Finding the equation of…

Q: The linearity between two variables X and Y, in pairs, defined as X=[4,2,3,5,2,4] and…

A: Linearity x y xy x2 y2   4 6 24 16 36   2 4 8 4 16   3 6 18 9 36   5 8 40 25 64   2 5…

Q: y 2+ 1+ (A) (3,1) (B) (2,1) (C) (2,-1) (D) (1.5,0.5) (E) (1,0) 0 -1 P 2 3 Q(3,2) In the figure…

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Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: 25. Determine the x- and y-intercepts. a) [x, y] = [2, –4] + t[3, –1] b) [x, y] = [-8, 11] + t[5, 2]…

A: The given equations are in parametric form. To find x-intercept put y=0 and get the value of…

Q: | Let w=z² Find the image of the first quadrant in Z-Plane 2

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Q: If A = 3a_0 + 2a_0 - 5a_z and B = -2a_p + 3a_0- a_z are given at points P(3,T1/6,5) and Q(4,T1/3,3)…

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Q: 16. Where does the smallest value f(r, y) + 3ay + y occur on the rectangle (-2, 2) x (-3, 1]? a) It…

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Q: Let I be the line passing through the point P=(3, -2, 1) with direction vector -[3, 2, -3]T. Find…

A: If we drop a perpendicular from a point P on a line  l then foot of perpendicular will be closest…

Q: Find the derivative of y = In{(7x³ + 4) V3x + 10}

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Q: Q5/A// Find the distance between the point P =(2, 1, 1) and line L:x = -2+ 5t, y= 2 +4t, z = -3-6t.…

A: Use distance formula

Q: Let x = (m , 1 , 0 , -2)", m > 0 and ||x|l2 = v30, then m = Select one: а. 4 b. 5 с. 6 d. 7

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Q: Find the distance from the point (-6, −6, 2) to the line Ỉ =(−1,−1,7)+t(4,−8,2),−oo <t<0. <∞.

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Q: 3. A line in the xy-plane passes through the point 늘 following points lies on the line? (1,-2) and…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.