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Answer:
The horse travels 31 feet over an angle of radians
Step-by-step explanation:
- The formula of the length of an arc is L =
× 2πr, where x is the central angle subtended by this arc and r is the radius of the circle
- To change the angle from radian measure to degree measure multiply it by
∵ A carousel horse travels on a circular path
- That means the distance that the horse travels is the length
of an arc of the circular path
∵ The radius of the circular path is 15 feet
∴ r = 15 ft
∵ The horse travel over an angle of radians
- Let us change it to degree by multiply it by
∵ ×
=
= 120°
- use the formula above to find the distance
∵ d = × 2πr
∵ x = 120°
∴ d = × 2π × 15
∴ d = 10π
∴ d = 31.41592654 feet
- Round it to the nearest foot
∴ d = 31 feet
The horse travels 31 feet over an angle of radians
Answer:
1. (7.4,3.6)
2. (3,-1)
3. (-2,-3)
4. Infinite number of solutions.
Step-by-step explanation:
We can solve systems of equations 3 ways: graphing, substitution, and elimination. We will solve 1-2, 4 using substitution and 3 with elimination.
1. Since x=4y-7, we substitute it in for x . It's better than elimination because of how it is set-up unless there is a typo.
- So -4x+4y=-8 becomes -4(4y-7)+4y=-8.
- We simplify to -14y+28+4y=-8.
- We add like terms to get -10y+28=-8.
- We now solve for y by subtracting 28 and dividing by -10.
- -10y+28-28=-8-28
- -10y=-36
- y=3.6
- We substitute y=3.6 into x=4y-7. x=4(3.6)-7=14.4-7=7.4
2. Since none of the coefficients of x & y are the same, we will rearrange and substitute.
- -8x+2y=-26 becomes 2y=8x-26 by adding 8x to both side.
- We divide by 2. y=4x-13.
- We substitute into -5x-5y=-10. -5x-5(4x-13)=-10
- We simplify to -5x-20x+65=-10
- We add like terms. -25x+65=-10
- We now solve for x by subtracting 65 and dividing by -25.
- -25x+65-65=-10-65
- -25x=-75
- x=3
- We substitute x=3 into -8(3)+2y=-26
- -24+2y=-26
- 2y=-2
- y=-1
3. We can solve this system through elimination. We subtract or add the equations when the coefficients are the same to eliminate one variable.
- We susbstitute y=-3 into one of the equations 3x-(-3)=-3.
- 3x=-6
- x=-2
4. Since none of the coefficients of x & y are the same, we will rearrange and substitute.
- -x+y=-2 becomes y=x-2
- We substitute into 4x-4(x-2)=8.
- Simplify 4x-4x+8=8.
- Add like terms 0x+8=8
- 8=8
- This is a true statement and a special solution. It means infinite number of solutions.