George is saving for a mortgage on a $125,000 house. He needs 20 percent for a down payment. He currently has $22,000. How long
2 answers:
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A cylinder with a circumference of about 50 units is formed.
Step-by-step explanation:
Step 1:
The perimeter of the square is 32 units. The perimeter of a square is given by 4 times its side length.
So the side length of the square is 8 units.
If a square is rotated a cylinder will be formed. So the options with a cone are wrong as a cone is formed when a triangle is rotated.
Step 2:
To calculate the circumference of the cylinder, we multiply 2π with the radius. The radius is the same as the side length of the square. So r is 8 units.
The circumference of the cylinder
So the circumference of the cylinder is approximately equal to 50 units so the answer is the fourth option, a cylinder with a circumference of about 50 units.
Answer: The correct options are
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
Step-by-step explanation: Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.
Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.
The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).
And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).
<u>Option (A) Rotation 90°:</u>
We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.
So, rotation of 90° anticlockwise is a correct option.
<u>Option (B) Rotation 180°:</u>
If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.
So, rotation of 180° is NOT a correct option.
<u>Option (C) Rotation 270°:</u>
If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.
So, rotation of 270° clockwise is also a correct option.
<u>Option (D) (x, y) → (–y, x):</u>
We see that the co-ordinates of both the triangle follow the transformation
X(0, 0) ⇒ X'(0, 0)
Y(0, -2) ⇒ Y'(2, 0)
Z(-2, -2) ⇒ Z'(2, -2).
So, the transformation is (x, y) ⇒ (-y, x).
Therefore, the transformation (x, y) → (–y, x) is a correct option.
<u>Option (E) (x, y) → (y, -x):</u>
We see that the co-ordinates of both the triangle does NOT follow this transformation
For example, suppose this transformation is correct. Then, we have
Y(0, -2) ⇒ (-2, 0), which are not the co-ordinates of Y'.
Therefore, the transformation (x, y) → (–y, x) is NOT a correct option.
Thus, the correct options are:
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
