Part A: What are the coordinates of A"B"C"D" if we reflect it over the line y=2, then dilate by a scale factor of 12 centered at the origin? A(8,12)→A'( )→ A"( B(10,4)→B'( )→ B"( C(4,4)>C'( )→ C"( D(2,8)→D'( )→ D"(

Q: 3) Find the maximum rate of change of f at the given point P and the direction in which it occurs.…

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2). Suppose that you…

A:

Q: Find the maximum rate of change of fat the given point and the direction in which it occurs. f(x, y)…

A: Note: where △f(x,y) = ∂f∂x,∂f∂y

Q: If a regression model is fitted for y against xy and xy and R is equal to 1, this necessarily means…

A: Step 1: The estimated regression equation can be written as y^=β0+β1x1+β2x2 Where, β0: Interceptβ1:…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given,

Q: The normal line at point P(0,a,-a) of the surface given by the equation F(x,y,z) = 3xyz – z' – a' =…

A:

Q: 9) reflection across the y-axIS

A: Png the reflection of the given graph across y-axis

Q: 2) Find the maximum rate of change of f at the given point P and the direction in which it occurs.…

A:

Q: (2) Let f(x, y) = x² – y². Find the tangent line to the level curve f(x, y) = -3 at (1,2).

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Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: The change in the relative configuration of point within a solid is called strain 0 صواب ihi O

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Tangent to the parabola z = x² + 3y² , x = 1 , at point ( 1, 2, 13

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

Q: 2. Let f(r,y) = n: Find the maximum rate of change of f(r, y) at the point (4, 1) and the direction…

A: Given the given function is fx,y=xx-y and the point is 4,1. Apply formula for the maximum rate of…

Q: 2/6 Consider the upper half of the ellipsoid f(x.y) = 1--n and the point P-- 3 on the level curve…

A:

Q: How many points are there on the surface 2 dx+y such that the tangent plane to the surface is…

A: We have given the a=6,b=9,c=9 d=max(a,b,c)=max(6,9,9)=9 The given surface is f(x,y,z)=9x2+y2-z We…

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: 5. The diagram shows the curve y = 3x - x and tangent to a the curve at point A passes point B.…

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Q: Verify that the point P(a cos 0, bsin 0) lies on the ellipse = 1. a2 where a and b are the…

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Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

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Q: 1. Find an equation of the tangent plane to the surface of z = sin(x - 2y) at the point (7,2,0).

A:

Q: e tangent line to the ellipse 25 = 1 at the point (x, y). 9. %3D s where the slope is not defined?…

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Q: A line passes through the point Po(xo, Yo) and has gradient m = tan a. Show that a general point of…

A: Gradient, or slope of a line characterizes the direction of the line and is found out by dividing…

Q: Sketch the region enclosed by the given curves. y = 2 cos(6x),    y = 2 − 2 cos(6x),    0 ≤ x ≤ π/6

A: Find the intersection points:

Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

A:

Q: 8. The temperature of the xy-plane is given by the function f(x, y) = x²y+e¬¤. (a) At the point…

A: The direction of maximum decrease of a scalar function f(x, y) is given by the negative of the…

Q: Find the maximum rate of change of fat the given point and the direction in which it occurs. f(x, у)…

A: Given function and point is

Q: b) Find equations for the tangent plane and normal line at the point P-(2, –3,18) on the surface…

A: x2+y-2xy-x+3y-z=-7   Let fx,y,z=x2+y-2xy-x+3y-z+7 and the point is 2,-3,18 Now,…

Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 8. y = 4x°(1– cx);

A: We have to solve

Q: 13. Find an equation for the tangent plane and the normal line to the surface x? + 2y? - 3z? = 3, at…

A:

Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…

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Q: Find the tangent plane to the graph of **yz +z'e* -y² = 5 at (1,3,2).

A:

Q: 2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, 3 are positive…

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Q: Find an equation of the tangent plane to the surface y ln xz2 = 2, at the given point (e, 2, 1) and…

A: Given: ylnxz2=2 at the given point e,2,1

Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

A:

Q: A/Find the distance between the line 2x + 3y = 5 and the point(-1,0). ( B/Find by integrating along…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Use a linear approximation to estimate the change in f(x,y, z) = e2" cos(5yz) when moving from the…

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Q: A line passes through the point P0(x0, y0) and has gradient m = tan α. Show that a general point of…

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Q: a.find the tangent plane to the implicit surface at the point (0, 1, 1) given ye"* + yz² = 2xy³ + 2…

A: We have Fx,y,z=yexz+yz2−2xy3So,the surface implictly is written as Fx,y,z=2Now…

Q: 22 2 Find the equation of the tangent plane to the level surface xy*z? (– 1, – 1, – 2) = 4 at the…

A:

Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 8. y = 4x*(1 – cx);

A: The given equation is y2=4x21-cx. Find the orthogonal trajectories of the given family of the curve.

Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

A:

Q: 3. Evaluate the gradient of S(1, y, 2) = In(cosh z+ y) - arctan| at (1,y) = (7/2, 1).

A: Given that fx,y,z=lncosh x+y-z2 arctanx2y2+z2 To find the gradient of f(x,y,z) :…

Q: Figure below shows the region and a cylindrical shell formed by rotation about the line x = 2. It…

A: The formula for the volume is: V=2π∫abh r dx

Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

Q: Integrate h(x, y) = (x+y)i+-x)j over the closed curve that begins at (-1, 0). goes along the x-axis…

A: Let me tell you , In this problem we are going to use Green's theorem. Note: Green's theorem is only…

Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)

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…

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.