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solong [7]
2 years ago
5

Mei draws three pairs of parallel lines that are each intersected by a third line. In each figure, she measures a pair of angles

.
What is a reasonable conjecture for Mei to make by recognizing a pattern and using inductive reasoning?


When a pair of parallel lines are intersected by a third line, the alternate interior angles are acute.

When a pair of parallel lines are intersected by a third line, all of the angles formed are obtuse.

When a pair of parallel lines are intersected by a third line, all of the angles formed are congruent.

When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.
Mathematics
1 answer:
alisha [4.7K]2 years ago
6 0

Answer:

The correct answer is When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.


Step-by-step explanation:

I just took the test.

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A projectile is fired with muzzle speed 220 m/s and an angle of elevation 45° from a position 30 m above ground level. Where doe
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Answer:

  • 4968.6 m from where it was fired
  • 221.33 m/s

Step-by-step explanation:

For the purpose of this problem, we assume ballistic motion over a stationary flat Earth under the influence of gravity, with no air resistance.

We can divide the motion into two components, one vertical and one horizontal. For muzzle speed s and launch angle θ, the horizontal speed is presumed constant at s·cos(θ). The initial vertical speed is then s·sin(θ) and the (x, y) coordinates as a function of time are ...

  (x, y) = (s·cos(θ)·t, -4.9t² +s·sin(θ)·t + h₀) . . . . . where h₀ is the initial height

To find the range, we can solve the equation y=0 for t, and use this value of t to find x.

Using the quadratic formula, we find t at the time of landing to be ...

  t = (-s·sin(θ) - √((s·sin(θ))²-4(-4.9)(h₀)))/(2(-4.9))

  t = (s/9.8)(sin(θ) +√(sin(θ)² +19.6h₀/s²))

For s = 220, θ = 45°, and h₀ = 30, the time of flight is ...

  t ≈ 31.939 seconds

Then the horizontal travel is

  x = 220·cos(45°)·31.939 ≈ 4968.6 . . . . meters

__

As it happens, the value under the radical in the above expression for time, when multiplied by s, is the vertical speed at landing. The horizontal speed remains s·cos(θ), so the resultant speed is the Pythagorean sum of these:

  landing speed = s·√(cos(θ)² +sin(θ)² +19.6h₀/s²) ≈ s√(1 +0.012149)

  ≈ 221.33 m/s

_____

Note that the landing speed represents the speed the projectile has as a consequence of the potential energy of its initial height being converted to kinetic energy that adds to the kinetic energy due to its initial muzzle velocity.

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