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Intersection and distance in three-dimensional space
49528 Intersection and distance 1. Find the intersection point of the line (x-1)/2=(y+1)/3=z-2 and the plane 2x+y-z=17.
2. Find the distance from point Q(1,-2,3) to the plane 2x-y-z=6.
Need steps and solutions.....Thanks! 1.
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Finding two numbers y such that the distance from (-2, 3) to (2, y) is 5.
78061 Finding two numbers y such that the distance from (-2, 3) to (2, y) is 5. Find two numbers y such that the distance from (-2, 3) to (2, y) is 5. Please see the attached file. Coordinates are calculated to match a distance btween two points.
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Linear Programming using the Corner Points Method
Our feasible region has the following vertices:
(2,3)
(5,0)
(8,0)
The values of the objective function at these points are
2*2+2*3=10
2*5+2*0=10
2*8+2*0=16
The minimum is achieved at two different points, (2,3) and (5,0), so we conclude that the
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Simple Prolog
- cube([5],[5,25,125]).
yes.
?- cube([2,3],[2,3,4]).
no.
• (5) In Prolog, implement the predicate dotProduct/3. This predicate will relate two vectors (represented as lists) to their dot product.
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Algebra: Slopes and Circles
(iv) Show that the line corresponding to the parametric equations x=t?2, y=?(3/5)t+2
is the same line as in part (a)(iii) above.
(b) Find the equation of the perpendicular bisector of the line segment AC.
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Equations of lines
Write an an equation of the line containing the given point and parallel to the given line. Express your answer in the form y= mx + b.
(2,3;x+4y=3
the equation of the line is y= .
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Discrete Math: Matching Zeros
There are 5 points in the big square means that there are at least two in any of those 4 small squares.
Let's say that on the left top small square there are 2 points. The distance between those two is at most equal to one of the diagonals.
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Hemicontinuity
Since r is an arbitrary point on [2,3], therefore, F is upper hemicontinuous on [2,3]
2) Proof:
Let's denote |x| as the distance of x.
For any point x in R^n{0}, let x_n->x and x_n belongs to R^n{0}. Let y_n belongs to F(x_n) and y_n->y.
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Solving a set of basic mathematical questions
Plug y=3 into (1) to get 2x+3=7, so x=2.
The graph is shown below. The intersection point (2,3) is circled.
12. Two people set out simultaneously from two locations 12 miles apart and walk toward each other.