Answer:
a. 11/5 pi; -9/5 pi
Step-by-step explanation:
Coterminal angles are those which have a common terminal side. For example 30° is coterminal with −330° and 390° (see figure).
From the example we can see that the following expressions must be fulfilled:
positive angle - reference angle = 360°
reference angle - negative angle = 360°
where positive angle is 390°, reference angle is 30° and negative angle is -330°. In this problem reference angle is pi/5. Also, we have to change 360° for its equivalent in radians, i. e., 2 pi. So,
positive angle - pi/5 = 2 pi
positive angle = 2 pi + pi/5
positive angle = 11/5 pi
pi/5 - negative angle = 2 pi
negative angle = pi/5 - 2 pi
negative angle = -9/5 pi
Right Triangles and the Pythagorean Theorem
The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , can be used to find the length of any side of a right triangle.
The side opposite the right angle is called the hypotenuse (side c in the figure).
Given that an animal shelter houses three kinds of animals: dogs, cats and rabbits and it has a total of 126 animals. 1/3 of the animals are cats. This means, 1/3 of 126 is 42. So there are 42 cats. 3/4 of the remaining animals, which is 84 are dogs. So 3/4 of 84 is 63. So there are 63 dogs. 63 dogs plus 42 cats is 105 animals. 126 minus 105 is 21. Therefore, there are only 21 rabbits. Hope this helps.
Answer:
- triangle
- square
- hexagon
- dodecagon
Step-by-step explanation:
The 12 points marked can be divided into this many equal-size groups:
3, 4, 6, 12
so the figures that can be constructed are ...
- triangle . . . . connects every 4th mark
- square . . . . . connects every 3rd mark
- hexagon . . . .connects every other mark
- dodecagon . . connects every mark
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12 is also divisible by 1 and 2, but the minimum number of vertices in a regular polygon is 3.
