List the sides in order from shortest to longest in AXYZ: with mZX = 50, mZY= 5x + 10, and mZZ= 5x. I|

Q: Find the point on the line x/a + y/b =1  that is closest to the origin. Be sure to enter it as an…

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Q: How find the pistance from fant (1,3) and Line y -4

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Q: use Eq. (3) to find the length of the path over the given interval. (3t + 1, 9 − 4t), 0 ≤ t ≤ 2

A: We have to find the length of the curve 3t+1,9-4t ,0≤t≤2

Q: Find the perimeter of a triangle with vertices S(4,5), T(-2,-3) and W(5,-4).

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Q: . Find the exact distance between P1 = ( - 1, - 7) andP2 = ( 2, - 1). Then approximate the distance…

A: We know that, the distance d between two points x1,y1 and x2,y2 is given as d=x2-x12+y2-y12…

Q: find the nature of triangle formed by the lines x2-3y2=0 and X=2

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Q: The midpoint of AB is at (- 4, – 4). If A = (0, 4), find B. B is:(

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Q: Find the point on y – axis which is equidistant from the points (3, 1, 2) and (5, 5, 2)

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Q: An object is traveling along a path described by y = x + 3. Where along that path will the object be…

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Q: Find the length of the chord intercepted by the circle x2+y2-x+3y-22=0 on the line y=x-3

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Q: Find x²z ds, where C is the line segment from (0,-5,4) to (2,-7,8)

A: C is line segment from (0,-5,4) to (2,-7,8). parametric equations of C are: r(t)⇀=(1-t)r0⇀+tr1⇀  ,…

Q: use Eq. (3) to find the length of the path over the given interval.  (1 + 2t, 2 + 4t), 1 ≤ t ≤ 4

A: Given  x, y=1+2t,  2+4t where dxdt=2, dydt=4 a 1≤t≤4.

Q: nded by the curve y2=4x and the lines x = 1 and x = 4.

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Q: Find the distance from the point (3, 9) to the line y = 2x.

A: To find the distance from the point (3, 9) to the line y = 2x.Observe that the slope of the given…

Q: Find | x²z ds, where C is the line segment C from (0,-3,2) to (-3,-2,8)

A: Given C is the line segment from (0,-3,2) to (-3,-2,8) Now write the parametric equation for C…

Q: Find a point on x axis which is equidistant from A(2,-5) and B(-2,9)

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Q: Find the length of the chord made by 3x? – y? = 3 and y + æ – 5 = 0. -

A: 3x2-y2=3    →1y+x-5=0    →2 From equation (2), we get y=5-x Now put y=5-x in equation (1), we get…

Q: use Eq. (3) to find the length of the path over the given interval. (2t2, 3t2 − 1), 0≤ t ≤ 4

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Q: points

A: Please refer to the image below

Q: The midpoint of AB is at (- 4, - 2). If A = (0, 10), find B. B is:(

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Q: Find | xz ds, where C is the line segment from (0,0,-6) to (-5,5,-7)

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Q: Find the Exact and approximate distance between the two points (7,2) (11,5)

A: The given two points are (7, 2) and (11, 5) The distance formula is given as:

Q: How far is the intersection of the lines 4x-5y=26 and 3x+7y+2=0 from the origin

A: We have to find the distance of the intersection of the lines 4x-5y=26 and 3x+7y+2=0 from the…

Q: Determine what is the minimum distance from the origin to the line  y=-2x+5

A: topic - distance of line from origin

Q: Find point P(x,y) if it is equidistant between points A(2,9) and B(-3,6)

A: Given:-  Px,y is equidistant  from the points  A2,9  and  B -3,6 i.e,  AP=BP and  we know  that…

Q: Find the equation of the Mane that contains the line 3X - 2:2 = - 39 = 7-7 and that is Para llel to…

A: When the plane is parallel to the line x-y+z=2: Here n1→=i^-j^+k^ and a→=2i^+3j^+k^ To find…

Q: If ∆MNP is reflected across the line y = 2, then translated using the rule (x + y) → (x – 8, y – 1),…

A: We have been given the coordinates of the point P(7, 4) using the rule  (x + y) → (x – 8, y – 1).

Q: Find a point on the line y = 2x 3 that is 5 units from the x axis. %3D

A: The given equation is, y=2x-3

Q: Find the shortest distance from the point (- 1, – 2, 5) to the cone z = x² + y². Please | round to…

A: Distance of a point from cone is                                      d=(x-x1)2+(y-y1)2+(z-z1)2 from…

Q: Find the values of δƒ/δx and δƒ/δy at the point (4, -5) ifƒ(x, y) = x2 + 3xy + y - 1.

A: ddxxn=n xn-1

Q: How is the line y = 1 converted by mapping w = e? ?

A: In this question, we convert the line y=1 by mapping w=e^z.

Q: Find the distance from the point (4, 9) to the line y = 2x.

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Q: Find the shortest distance between the point Q (2, 0, 0) and the line determined by the points P1(0,…

A: Find the shortest distance between the point Q (2, 0, 0) and the line determined by the points P1(0,…

Q: Find the point on the line y = 4x + 3 that is closest to the origin. (х, у) %3D

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Q: use Eq. (3) to find the length of the path over the given interval. (3t2, 4t3), 1≤ t ≤ 4

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Q: Find xz ds, where C is the line segment from (0,-2,4) to (0,-6,1).

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Q: 9. Solve for x and y that make the lines parallel.

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Q: Construct three parallel lines so that the middle line is not equidistant fromthe other two. Then…

A: Let the three parallel lines be l, m, n and the equilateral triangle be ABC.

Q: For the rectangle windows whose L(-3,-2) and R(2,3), Find the intersection point for X(-1,1) to…

A: Given rectangle windows has: Lower left hand corner at Upper right hand corner at To find: The…

Q: Find all points on the y-axis that are 5 units from the point (4, 4).

A: Distance between two points (x1,y1) and (x2,y2) on the graph is given by the distance formula, that…

Q: What is the range of possible sizes for side x?

A: Consider the third side be x. Apply the fact that the sum of any two sides of a triangle must  be…

Q: Solve for side Y for triangle XYZ X=85°, Z=46°,x=19

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Q: Find x²z ds, where C is the line segment from (0,6,4) to (1,3,-2) C

A: ∫C y ds,  C: x=t2, y=t,  -2≤t≤3   dxdt = 2t,   dydt= 1∫Cy ds = ∫-23 t  (2t)2+1 dt=∫-23 t  4t2+1…

Q: DETERMINE THE SHORTEST DISTAtNCE FROM THE POINT -1,2) 5x-12y=10, TO THE EQUATION %3D

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Q: Find two numbers y such that the distance from ( - 3, 2) to (5, y) is 10.

A: To find: The value of y. Given: The distance between the two points -3,2 and 5,y is 10. Concept…

Q: An object is traveling along a path described by y =x +3. Where along that path will the object be…

A: Given: An object is travelling along a path described by y=x+3.

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.