21x>2 should be the answer
The coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° counterclockwise include the following:
U' = (1, 1).
V' = (-4, 0).
W' = (-1, 4).
In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of triangle UVW, the coordinates of the vertices of the image are as follows:
(x, y) → (-y, x)
Ordered pair U = (-1, 1) → Ordered pair U' = (1, -(-1)) = (1, 1).
Ordered pair V = (0, -4) → Ordered pair V' = (-4, -(0)) = (-4, 0).
Ordered pair W = (-4, -1) → Ordered pair W' = (-1, -(-4)) = (-1, 4).
Read more on rotation here: brainly.com/question/28854313
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v^2 - 18v + ?
Answer: (v - 9)^2 - 81
Step-by-step explanation: Use the formula (b/2)^2 in order to create a new term to complete the square.
Hope this helps! :) ~Zane
how?
Answer:
see explanation
Step-by-step explanation:
using the identity
cos²x = 1 - sin²x
consider the left side
multiply numerator/ denominator by (1 + cosx)
= ← expand numerator
=
= ← cancel sinx on numerator/ denominator
=
= right side , thus proven
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Final answer:
The question pertains to finding theclosest point on a plane to a specific point and determining the local extremum points of a function using differential calculus. Due to word limitations, a step-by-step solution couldn't be provided.
Explanation:
The subject of this question is Mathematics, specifically it deals with the concepts of planes in three-dimensional space and finding local extremum points of a function. Firstly, to find the point on the plane x - 2y + 3z = 12 closest to the point (0, 2, 2), we can use the perpendicular distance formula from a point to a plane. To find the local maximum, minimum values and the saddle points of the function F(x, y) = -y − by cos(x), differential calculus should be used. Unfortunately, this requires more than 100 words, therefore I am unable to provide a step-by-step solution here.
Learn more about Differential Calculus and Plane Geometry here:
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