Exercise I: Fruit ninja 1. Determine the surface S given by the equation x 2 − 4x + y 2 − 2y + z 2 − 6z = 2. 2. Find an equation of the plane P going through the points (1, 1, 1), (1, 4, −2), and (−1, 0, 4), of the form ax + by + cz + d = 0. 3. Clearly, the intersection of S and P is a circle. Compute the radius r of this circle. You may want to draw a picture first, and use a result seen in class!

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Detailed solution on the attached pictures

$5.41

step-by-step explanation:

$20 - $14.51 = $5.49.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: