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1 answer:
Answer:
Please check the attached figure!
Step-by-step explanation:
Part a)
Point A is located at the x-coordinate x=-4 and y-coordinate y=1.
Hence, the coordinates of point A = (-4, 1)
Part b)
Point B(3, -2) has been plotted and is shown in the attached figure.
It is clear from the attached diagram that point B is located at the x-coordinate x=3 and y-coordinate y=-2. Hence, the coordinates of point B = (3, -2)
Part C)
Point C has the same x-coordinate as point A i.e. x=-4 and the same y-coordinate as point B i.e. y=-2.
Hence, the coordinates of point C = (-4, -2). Point C is also plotted as shown in the diagram.
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Answer:
refer to the attachment please
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Answer:
Step-by-step explanation:
We are given that the cost function is given by
We have to find the rate of decrease of this function at the point
Greatest rate of decrease of this point at the point is given by
The position vector of P and Q is P = ( 6 i -3j +9k ) , Q = ( 3i -6 j -3k) , the coordinates of R is ( 5 , -4 , 2)
<h3>What is a vector ?</h3>A vector is an object with both mass and magnitude.
It is given that
The coordinates of
P (6, -3,9 ) and Q (3, -6, -3)
point R divides line PQ internally in the ratio 1:2.
The position vectors of P, Q and R is given by p, q and r respectively.
The position vector of P and Q in terms of i, j, k is is
P = ( 6 i -3j +9k ) , Q = ( 3i -6 j -3k)
The magnitude of P =
|p| = 11.224
The magnitude of Q =
|q| = 7.348
The coordinate of R is
if a point (x,y,z) divides the line joining the points (x₁,y₁) ) and (x₂ ,y₂) in the ratio m:n, then
( x, y, z ) =
The m : n = 1 : 2
(x,y,z) =
(x,y,z) = 5 , -4 , 2
Therefore the coordinates of R is ( 5 , -4 , 2)
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