Find the the point on the line l: +t 0 | closest to the point P(3, 2, –2). ||

Q: Z is the midpoint of VY and X is the midpoint of WY. If VW = s + 47 and XZ = s, what is the value of…

A: Given,          Z is the midpoint of VY¯ and X is the midpoint of WY¯ .           VW=s+47 and XZ=x…

Q: The spread of a virus is modeled by V(t) = -t° +t² + 12t, where V(t) is the number of people (in…

A:

Q: Find the abscissa on the curve x²=2y which is nearest to a point (4, 1). А. 0 С.2 В. 1 D. 3

A: Use the distance formula then minimise using derivative.

Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

A:

Q: Find the convolution f (t ) *g(t) f(t)=t^2,g(t)=cost

A:

Q: Find F(s). F(s) = £{t(et + e5t)2}

A:

Q: Find the linear approximation to the equation f(x, y) = 3, zy at the point (6,2,6), and use it to…

A:

Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the exact length of the curve. y - 4 + 2x 3/2, o sxS1 1.547

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

A:

Q: Q1. Find the length of the of the curve y -x2 X2 from x = 0 to x = 3.

A: Given curve is, y=13x32-x12 To find the length of the curve from x = 0 to x = 3

Q: Where does the line x = 1 + t, y = 3−t, z = 2t intersect the cylinder x² + y² = 16?

A:

Q: Q5) Find the coefficients a, b,c and d such that the curve defined by; y = ax3 + bx² + cx + d,…

A:

Q: For the equation, xt+1=rxt(1-xt) for t=0,1,2,... Find the two fixed points. For which values are…

A: To find: The two fixed points, which values are the locally stable. Given: The equation is…

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Find the point at which the line f(r) = -z+1intersects the line g(z) = 4x +1 %3D

A: At point of intersection both the functions will have the same value therefore f = g

Q: Q6) Find the distance from the point S= (1, 2, 1) to the line x = 2 -t, y=-1 + 2t, and z= 2 + 2t.

A:

Q: The area, in square units, between the curve y = 4|x and the x-axis on the interval [-3,4] is…

A:

Q: Find the linear approximation at x=0 √(7−x). Write your answer in the form y=Ax+B.

A:

Q: Find the length of the curve. y= (16-x2/3)3/2 from x=1 to x=64

A:

Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

Q: At how many points do the curves r₁ (t) = ((t+1)², -t2- 2t, t+2) and r₂ (t) = (1 − t², t, t)…

A: This is the problem of parametric equations and the theory of curves.

Q: f (x) = 0, %3D pendently selected, find the E

A: The number of sample is n=4. a. The probability of impurity weights exceeds 0.5 is,…

Q: a find theistance fron. the Point P(2,17 to the Line yzメ+22L

A: Line :- x+2-y=0  Point (2,1)

Q: Find the length of the curve r= e2θ, 0≤θ≤2

A:

Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: find the value of c that the line y=3/2x+6 is tangent to y=c(sqr-root x)  c=

A:

Q: 3 Find the length of the curve y = x² – 2 from x = 0 to x = 4.

A: Given curve is y=x32-2 Upon differentiating we get dydx=32x12 We know that length of…

Q: Find the value of n in the function w = x •rn satisfies the equation Wxx + Wyy = 0, where r2 = x² +…

A:

Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: Find the length of the curve y x7 from ¤ = 0 to x = 15. 2/3

A:

Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

A:

Q: Find the length of the curve x=e^t -t, y=e^(t/2), -8 less than or equal to t less than or equal to 3

A: The arclength for parametric curves is: L = ∫ab(dxdt)2+(dydt) Given  x=et-t, y =et2,      -8≤t≤3

Q: Q: Find the point on the curve 4x' +a'y = 4a', 4< a < & that is farthest from the point (0,-2).

A:

Q: Find Line in the plane of the points the PCO 10,0) ,Q (e,2,0) and R Coul,-d thal- passes through Q f…

A:

Q: ƒ(x, y) = 4x - 8xy + 2y + 1 on the triangular plate bounded by the lines x = 0, y = 0, x + y = 1 in…

A: Given function f(x, y),f(x, y) = 4x-8xy+2y+1             ........................(1)Given conditions…

Q: Q4/ Find the length of the curve y () (x² + 2) from x 0 to x= 3.

A: The length of a curve f(x) on an interval [a,b] is: L=∫ab1+(f'(x))2dx Where f'(x) is the first…

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

A:

Q: H.W: Find the distance from the point S(0,0,12) to the line L: x = 4t , y =-21 , z= 21 : =

A: According to the problem, we have

Q: స్థాగ The length of the curve y = Ex3/2 between x = 0 and x = 1 is %3D 2/3

A: Length of the curve=∫ab1+f'(x)2dxy=f(x)=23x32f'(x)=23×32x12=xf'(x)=xLenth of the curve between x=0…

Q: Q1. Find the length of the of the curve y = from x = 0 to x = 3.

A:

Q: n of the curve, L. (x+ 1)* , 0 0

A:

Q: Find the linear approximation at x=0 to √17−x. Write your answer in the form y=Ax+B.

A: we have f(x)=17-xDifferentiating both side w.r.t "x"f'(x)=-1217-x-12f'(x)=-1217-xput x=0f'(0)=-1217…

Q: For the function f(a, y) = wy - 2, we have f(2, -1) = -6. Use a linear approximation to estimate…

A: Solution of given problem is given as:

Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

A:

Q: Find the length of the curve y =1+6x?on the interval 0<x<1.

A:

Q: Q2: Find the distance from the point R( 2,2,10) to the line: x=t y=1+t z = 3-t

A: Here first we select a general point on the line Now, we find the direction vector of that point to…

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.