Given:
Point (7,12) is rotated 1260° counterclockwise about the origin.
To find:
The x-coordinate of the point after this rotation.
Solution:
If a point is rotated 360 degrees then its coordinates remains unchanged.
If a point is rotated 180 counterclockwise about the origin degrees, then
We know that,
After 
rotation the coordinates of points remains same, i.e., (7,12). So, after that (7,12) is rotated 180° counterclockwise about the origin.
The point (7,12) becomes (-7,-12) after rotation of 1260° counterclockwise about the origin.
Therefore, the x-coordinate of the required point is -7.
By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.
<h3>How to prove this point lies on the unit circle?</h3>
In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 120
Reference angle = 60°.
For the coordinates, we have:
sin(-120) = -sin(60) = -1/2.
cos(-120) = -cos(60) = -√3/2.
By applying Pythagorean theorem, we have:
z² = x² + y²
z = √((-1/2)² + (-√3/2)²)
z = √(1/4 + 3/4)
z = √1
z = 1.
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Answer:
Prism
B- A triangle cannot be "two polygons"
C- A cube also cannot be "two polygons"
D- A pyramid is not parallel.
Ok so go to the top left and multiple it by 0 and then you will still get 0 so -0 + 10x 4
The volume of the hockey puck will be 111.82 cubic cm.
<h3>What is volume?</h3>
Volume is defined as the space occupied by any object in the three-Dimensions. For the cylindrical shapes, the volume will be calculated by using the radius and the length of the cylinder.
Given that:-
- A hockey puck has a radius of 3.7 cm and a thickness of 2.6 cm
The volume of the hockey puck will be calculated as:-
V = π r² l
V = π ( 3.7)² 2.6
V = 111.82 cubic cm.
Therefore the volume of the hockey puck will be 111.82 cubic cm.
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