Question 6: How many different paths in the xyz-space are there from (0,0,0) to (3,4,5) if a path proceeds one step at a time by going either one step to the positive on the r-axis, one step to the positive on the y-axis, or one step to the positive on the z-axis? Justify your answer.

Q: A Swiss watchmaker wants to create a production plan for the next 4 months. Projected orders for the…

A: To formulate a linear program to determine the optimal amount to produce in each month while…

Q: 1. Find an equation of the plane that passes through the points (-1, 3, -3), (4, 1, 2), and (8, 2,…

A:

Q: Two ships pursue straight-line courses at steady speeds. At each time t (in hours, where 0 ≤ t ≤ 9),…

A:

Q: Does either of P = (4, 11, 20) or Q = (-1, 6, 16) lie on the path r(t) = ( 1 + t, 2 + t 2, t 4)?

A: Given rt=1+t,2+t2,t4

Q: Prove that the equation S =x+4xy+3y²– 4x – 10y +3=0 represents a pair of lines and find the…

A: Given equation is  S≡x2+4xy+3y2-4x-10y+3=0.   Since, the general equation  ax2+2hxy+by2+2gx+2fy+c=0…

Q: Find k so that the line through (– 3,2) and (k,4) is a) parallel to 5y- 2x = 1; b) perpendicular to…

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Q: A two-dimensional robot arm "knows" where it is by keeping track of a "shoulder" angle a and an…

A:

Q: Evaulate ∫C▒1/sinzdz , Where C is the rectangle with vertices at -1-i, 8-i,8+i and -1+i oriented…

A: Consider the provided question, The given rectangle with vertices is drawn as,

Q: Let R denote the rectangle with corners (−1, −2), (4, −2), (4,1), and (-1,1), and let P denote the…

A:

Q: 33 What point on the line through (1,2, 5) and 3, 1, 1) is closast to the point (2, -1, 5)?

A: Given: The line passing through the points 1,2,5 and 3,1,1 To find: The point on the given line…

Q: Each of the following equations defines a geometric object in 3-space. Describe in words what the…

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Q: Show that (-6,0) -10,-1) independent of path: af |ss|8 dy ag əx = = (-6,0) (-10,-1) (-6,0) (-10,-1)…

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: 11. In each part, solve the linear system, if possible, and use the result to determine whether the…

A: To Solve Linear equations,Multiply coefficients of one of the variable with each other and then add…

Q: If the line joining the two points (5,4)(5,4) and (3,−k)(3,−k) is parallel to the line kx−9y+11=0…

A:

Q: What is the dual of the phrase “three collinear points and a fourth point not on the line of the…

A: Answer :  Dual of any phrase can be find by replacing the conjunction connective with disjunction…

Q: The time spends for driving from point A to point B is linearly related to the number of cars on the…

A: For the solution follow the next step.

Q: 3. Let Path A denote the straight line segment from (0,0,0) to (1,1, 1). Let Path B denote the…

A:

Q: What is the orthogonal trajectory of

A: Orthogonal Trajectories : A curve which cuts every member of a given family of curves in accordance…

Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: A plane through the three points P = (4, -3, 5), Q = (-2, -3, 5), and R= (-2, 3, -3) is described by…

A:

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: The Vertex and the value of p'of the given parabola (x – 4)2 = 12(y – 7) are | - Vertex = (-4, –7);…

A: Use vertex form of parabola

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: Find two linearly independent solutions of y" +9ay=0 of the form 3₁=1+a3a³+a6z6+... y2 = x+b₁x+b7x7…

A: The given differential equation .We have to find the solution of the differential equation using the…

Q: 4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the…

A:

Q: Consider the integer points on the xy-plane. How many paths are there from (0,0) to (4,-2)? Only…

A: Consider the integer points on the XY plane. To find paths from (0,0) to (4,-2). Here only down and…

Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: 7. The line through the points and (2, 1, –3) Answer + 1 x = 2 + 2t, y =1+ t, z = -3 - 4t; (x – 2)/2…

A: The given point is: 0,12,1, and 2,1,-3 To find the equation of the line.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.