What are the new coordinates of the point (-14, -24) under the dilation (x, y) (0.5x, 0.5y)? O (-7, -12) O (-7, -24) O (-7, -14) O (-14, -12)

Q: Find the points where the tangent is parallel to y=0. y=x*-8x°+22x2-24x+9 O E 0 (1,1),(2,2),(3,0) O…

A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

Q: Find the acute angle between the curves y = (/3)x3, and y = (/3)/5 x at the point of intersection…

A: The given curves are y=3 x3 and y=35x=15x and the point of intersection of the two curves are P1, 3.…

Q: find a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

A:

Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: Suppose XY has coordinates X( -2, 5) and Y(3, -9). What are the coordinates for the midpoint of XY?

A: To find the Midpoint of the line.

Q: What are the new coordinates of the point (-5, 25) under the dilation (x, y) - (2x, 2y)? O (-10,…

A:

Q: he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20…

A:

Q: First try was incorrect Find the distance between points X and U. U +++ + -0.5 -0.3 0.5 -0.1 0.1 0.3…

A:

Q: Evaluate the length of the curve x = 5 - y+1,0<y<3

A: Given, x=5-y+1 ,     0≤y≤3

Q: What is the ALGEBRAIC RULE for REFLECTION over the y-axis? (х, у) —

A: Use reflection rule

Q: What is the maximum slope of f(x,y,z)=yex-x2sin(z) at the point (0,7,5)?

A:

Q: What is the maximum slope of f(x,y,z)=ye^x-x^2sin(z) at the point (0,7,-3)?

A: Given the function fx,y,z=yex-x2sinz and the point 0,7,-3. Computing the partial derivatives,…

Q: Evaluate (x+ y)ds where C is the straight-line segment x = 3t, y = (12 - 3t), z = 0 from (0,12,0) to…

A: We need to evaluate the integral along the given line. First eliminate the parameter t.

Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

A:

Q: Find the distance between the points (2, -- and (F,5 Distance- Preview(Round your answer to two…

A: Formula for calculating the distance between two points (x1,y1) and (x2,y2) is the squareroot of…

Q: What is the ALGEBRAIC RULE for REFLECTION over the line y = x? (х, у) —

A: This question is related to reflection of coordinates, We will solve it using given information.

Q: Approximate fx(1,3) using the contour diagram of f(x,y) shown below.

A: We can estimate fx by observing that as x goes from 0 to 2, with y = 3 fixed, fseems to go from…

Q: b) Find the shaded area of diagram that shecked by curve y =x² + 2x and the line y

A: The area between curves y=f(x) and y=g(x) on an interval [a, b] where f(x)≥g(x) on the interval is…

Q: What are the coordinates of the image D(0.5, R)(1, 3) where R(–3, 5) is the center of dilation?

A: What are the coordinates of the image D(0.5, R)(1, 3) where R(–3, 5) is the center of dilation?

Q: How will the contour maps of f (x, y) = x and g(x, y) = 2x with contour interval 1 look different?

A: To describe how the contour maps of f(x, y) = x and g(x, y) = 2x with contour interval 1 look…

Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: What relationship do you see between the segments of the median that are formed by the centroid?

A:

Q: and the line perpendicular to Find the area of a triangle bounded by the y axis, the tine f(z) - 9 -…

A: We have to find the area of the region bounded by the y-axis, the line f(x)=9-67x, and the line…

Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

A: Suppose that Y is random variable that takes on only integer value 1,2,.. and has distribution…

Q: Determine the center and the radius: X2 + Y2 + 2X +10Y + 1 = 0 O (-1,-5) Radius 5 O (1,5) Radius 5 O…

A: Topic-circle

Q: PQ lies in the standard (x, y) coordinate plane. What are the coordinates of the midpoint of PQ if P…

A: We need to find the coordinates of the midpoint of PQ¯ if P is located at -7,-11 and Q is located at…

Q: Evaluate the length of the curve x = 6 – Vy – 2 , 3< y<6

A: To find the length of following curve  x = 6 - sqrt( y - 6) 3 ≤ y ≤ 6

Q: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

A:

Q: Sketch the contour plot of f(x, y) = 4x² + y² using level curves of height k = 0, 1, 2, 3, 4, 5.

A: Given: f(x,y)=4x2+y2 Let 4x2+y2=k. Now graph contour plot for k=0,1,2,3,4,5.

Q: 10. Two corners of auxiliary rectangle at (-4,-7) and (0,0), vertical transverse axis

A: The diagram of the hyperbola having given conditions is shown below. Calculate the center of the…

Q: Suppose you are standing on the surface z = ƒ(x, y) at the point (a, b, ƒ(a, b)). Interpret the…

A: Given that a person standing on the surface z = ƒ(x, y) at the point (a, b, ƒ(a, b)).

Q: The line through the origin whose projection on the xy-plane is a line of slope 3 and whose…

A: In this type of questions we assume a line an points on that line. Suppose we have a line and points…

Q: What are the new coordinates of the point (-10, 10) under the dilation (x, y) (4x, 4y)? O (40, 40) O…

A:

Q: Haw J Express the fallasing function by Cartesian equationst 3K34tane Seco

A:

Q: Find the line through (1,-1,1)and normal to the line  3x=2y=z , and parallel to the plance  x+y-z=0…

A: Equation of the line: The equation of a line passing through the point (x0, y0, z0) is given by (x,…

Q: Rule: (x, y) → ( Reflection: Across Line y = x

A: Actually the rule of reflection along y=x is simply writing the points (x,y) as (y,x). See for the…

Q: Find the length of the curve x = (y − 5)3/2 from y = 5 to y = 6.

A:

Q: Find the tangent plane to the equation z = x2 + 5y² + 3y at the point (-5,-2,39)

A:

Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

A:

Q: 1 y == (x² + 4)°%2 ,0 sxS 2 (x2 + 4)°/2 ,0<x< 2 6. deur die berekening van die volgende bej…

A: The given function y is - y = 16x2+432     ........(1)Formula for calcualting the lenght of a curve…

Q: integral that line x = 0

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…

Q: 8. y- -x+4 , x=0, y=o, about the (x 20) y axis

A: y=-x2+4 and x≥0 ,x=0,y=0 about y axis

Q: What are the new coordinates of the point (3, -4) under the dilation (x, y) (0.25x, 0.25y)? O (3,…

A: We have to find the new coordinates of the point (3,-4) under the dilation (x, y) ----&gt; (0.25x,…

Q: What are the coordinates of the points in the graph of y? - r + 6z – 13 = 0 in which the tangent…

A: Tangent is horizontal at that point where derivative of function of zero

Q: Find the linearization of the function z =/ at the point (-5, 1). L(1, y)

A:

Q: Evaluate | xyzdx + In(xy)dy + xzdz over the straight line segment from (2, 1, 1) to (–1,1, –2)

A: We need to evaluate integral∫Cxyzdx+lnxydy+xzdz over the line segment from 2,1,1 to -1,1,-2.

Q: 23/ Find the angle between two curves: 3 y = 2 - x² , y = x²

A: The angle between two curves is given by the formula tan θ=f2'x0-f1'x01+f1'x0f2'x0 Given,…

Q: What are the new coordinates of the point (18, 8) under the dilation (x, y) → (1.5x, 1.5y)? O (32,…

A: Given the co-ordinates (x,y)=(18,8)

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.