Consider the integer points on the xy-plane. How many paths are there from (0,0) to (4,-2)? Only ‘down' and 'right' movements are allowed. Explain.

Q: *5. Prove that no two lines in hyperbolic geometry are equidistant from one another by showing that…

A: To prove that no two lines in hyperbolic geometry are equidistant from one another , first we…

Q: Find the distance from the point (-5, -1, -3) to the plane 5x + 3y + 2z = 1

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Q: Evaluate the line integral 6ydx + 4xdy where C is the straight line path from (2, 3) to (5, 5). Jc…

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Q: Find an equation for the plane in R³ spanned by the points (1,5,

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Q: The plane passes through the point (18, -16, 9) and contains the line given by = = z . 1.

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Q: Q2: The plane is divided into a finite number of regions by drawing infinite straight lines in an…

A: Let n denote number of lines drawn on plane. We will prove the result with the help of mathematical…

Q: Find the distance from the point Q(1, 2, -4) to the plane 2x - 5z = 5.

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Q: Which point is one fourth of the way between point A and point B on the line segment AB shown on the…

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Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3 are parrallel.

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Q: The line through the points (−3, 8,−4) and (1, 0, 8) intersects the yz-plane at _____.

A: We know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

Q: The set of all points in a plane that are equidistant from a fixed line and fixed point is…

A: The set of all points in a plane that are equidistant from a fixed line and fixed point is a/an…

Q: The set of all points in a plane the sum of whose distances from two fixed points is constant is…

A: We have to fill the blanks The set of all points in a plane the sum of whose distances from two…

Q: Rotate the point -320° to within 10°. (о, 1) x (1, 0) (-1, 0) (о, -1)

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Q: In a classic video game, balloons travel from left to rie linear path change as players repeat the…

A: Given,         (x-2)2+(y+3)2=4                          ...(1)

Q: Find an equation of the plane consisting of all points that are equidistant from (0, -5, 2) and (-5,…

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Q: Find the distance from the point (3, -4, 2) to the a. xy-plane b. yz-plane  c.xz-plane.

A: a) Distance of (3, -4, 2) from xy plane:On xy plane , z=0. So, This point is 2 units away from the…

Q: The distance between the point (9, 8, 3) and the plane x + y−2z = 5 is _____.

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Q: Sketch a graph of the plane x + z = 6 and label any intercepts.

A: given equation of plane is x + z=6 we have to find intercept of above plane put y=z=0 in above plane…

Q: What is the locus of points in your classroom that are 1 m from the floor?

A: The given information is "The locus of the points one meter from the floor" The below figure shows…

Q: Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: The plane containing the point (0,7,-2) and parallel to the plane -x + 8y + 6z = Ax+By+Cz = D. 4 has…

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Q: Find a plane containing the point (- 5, – 5, 2) and the line r (t) = (1, – 2, 1) + t(4, 7, 5).

A: Given that the required plane passes through the point P=(-5,-5,2) and required plane contains the…

Q: find the distance in space between the points (5,3,-2) and (0,0,1)

A: Use distance formula between two points

Q: Let S be a set of five distinct points in the plane with integer coordinates. Show that the midpoint…

A: Given S to be set of five distinct points in the plane with integer coordinates. Let the coordinates…

Q: The shortest distance from (−7,6,−8) to the xy-plane is

A: Since the plane is a xy-plane so, the point will be (-7,6,0).

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: Find the equation of the plane con taining the points Р(4, -1, 3) Q(1, -2, -1) and R(1, 0, 8)

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Q: Find the distance from the point (-3, 4, -1) to the plane 5x−4y−5z=−3.

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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: Find the distance from (-5,9, –12) to each of the following: 1. The xy-plane. Answer:

A: Given point :-  (-5,9,-12) To find:- Distance of given point to plane xy

Q: Suppose that point C lies in plane X and point D lies in plane X. What can you conclude regarding…

A: What can you conclude regarding CD↔.

Q: Where does the line through  (−3, 1, 0) and (−1, 7, 8)  intersect the plane  2x + y − z = −2?

A: Given : Points : ( -3 , 1 ,0) and ( -1 ,7,8) Plane : 2x + y - z = -2

Q: Find the general quation of plane containing the point P(-1,3,3), and perpendicular to the line…

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Q: The distance from the point K(3, -2, 0) to the xy-plane is Select one: 3 -2

A: Find out the correct option.

Q: Datermine whether the graphs of y = 7x + 2 and 7x – y = 0 are parallel, perpendicular, or neither. v…

A: The slope-intercept form of a line is given by y=mx+c, where m is the slope of the line and c is the…

Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: Hiwed Find equations for_thefallawing lines - The line through (3, Sz=2) Perfendiculor toX-z plane

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Q: What are the projections of the point (6, –3, 5) on the coordinate planes? On the xy-plane: ( On the…

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Q: Determine the distance from point Q = (2, 6, 9) to the plane x + 2y + 2z = 8

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Q: To avoid collisions with invasive species of aliens, new imperial regulations allow only positive…

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Q: Find all points where fex)= |21x-131 fails be be differenbiadle

A: Given:- f(x) = |21x-13| To find:- All points where function non differentiable

Q: Write the equation of the plane passing through point (3, 8, 3) that is parallel to the xz-plane.. X…

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Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: 13. . There are 8 points in a plane out of which 3 are collinear. How many straight lines can be…

A: There are 8 points in a plane out of which 3 are collinear and 5 are non collinear points.

Q: Show that the set of all points P, that are twice as far from (-1,5,3) as from (6,2,-2) is a sphere.…

A: Let's find.

Q: Find the points at which the line that passes through (–6,6,4) and (12,–6,2) intersects the three…

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Q: What is the significance of arrows along a plane curve?

A: What is the significance of arrows along a plane curve?

Q: What are the coordinates of the point on the directed line segment from (–10, –1) to (10,-6) that…

A: If a point on the directed line segment from (x1, y1) to (x2, y2) partitions the segment into a…

Q: The plane containing the three points (2, –1, –1), (2, 1, 8) and (1, 0, 6). Please write th

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Q: Find the distance from the point (-1,4,5) to the plane 3x+2y-4z=5?

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.