Question

A water grist mill has a radius of 9ft and takes 8 seconds to make a complete rotation. a bucket starts at position (9,0). what are the coordinates of the bucket's location after 6 seconds? round values to the nearest tenth.

Answer 1

If the grist mill completes the rotation in 8 seconds. Then the final position of the bucket after 6 seconds is (0, 9).

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

A water grist mill has a radius of 9ft and takes 8 seconds to make a complete rotation. a bucket starts at position (9,0).

Then the coordinates of the bucket's location after 6 seconds will be

The angle of rotation after 6 seconds will be

$\rightarrow \dfrac{6}{8} \times 360\\\\\rightarrow 270^o$

Then we have

x = 9 cos 270°

x = 0

and y will be

y = 9 sin 270°

y = -9

But the angle is in a clockwise direction, then

y = 9

More about the coordinate geometry link is given below.

brainly.com/question/1601567

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Answer 2

Answer:

(0, −9.0)

Step-by-step explanation:

6 seconds is 68 of a complete rotation.

Calculate the angle of rotation.

68(360∘)=270∘

The rule for this particular rotation is: (x,y)→(y,−x).

This rotation changes all x distances into y distances, and all y distances into x distances of the opposite sign.

The figure shows three points on a Cartesian plane. Point A is at nine, zero. Point B lies on the negative direction of y axis. Point O is at the origin. Angle A O B measures 270 degrees. Segment O B has a length of 9 units. The angle is highlighted in red.

Apply this rule to the point (9,0).

(9,0)→(0,−9).

Therefore, the coordinates of the bucket's location after 6 seconds are (0,−9.0).