The answer to your question is the last one.
<span>Using radian meansure
theta = (arc length)/radius
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arc length = radius*theta
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Your Problem:
120 degrees = 120(pi/180) = (2/3)pi radians
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circumference = 2pi*r
24 = 2pi*r
r = 12/pi
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arc length = (12/pi)(2/3)pi = 8 units
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Formula for triangle area = base times height over two. area of smallest triangle: 2*2/2, so 2. area of medium sized triangle: 2*6/2, so 6. the square in between those triangles has an area of four (2*2). the base of the largest triangle is 2+2+6, so 10, and the height is 4. use the formula to find its area is 20. add them all together to get 4+6+4+20 is 34 units^2.
Answer:
Step-by-step explanation:
Michael and Juanita are interested in the amount of sand required to build a sand pyramid of the size that they see while at a sand sculpture exhibit. They carefully measure the width of the square base of the sand pyramid which is 4 feet and the height of the pyramid which is 5 feet. How much sand is required to build this sand pyramid?
Answer:
- The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is <u>translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis</u>.
Explanation:
By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.
You can check that analitically
Departing from the triangle: XYZ
- <u>Translation 5 units to the left</u>: (x,y) → (x - 5, y)
- Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)
- Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)
- Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)
- <u>Translation 1 unit down</u>: (x,y) → (x, y-1)
- (-11,2) → (-11, 2 - 1) = (-11, 1)
- (-9,7) → (-9, 7 - 1) = (-9, 6)
- (-7, 2) → (-7, 2 - 1) = (-7, 1)
- <u>Reflextion accross the x-axis</u>: (x,y) → (x, -y)
- (-11, 1) → (-11, -1), which are the coordinates of vertex X"
- (-9, 6) → (-9, -6), which are the coordinates of vertex Y""
- (-7, 1) → (-7, -1), which are the coordinates of vertex Z"
Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.
