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emmainna [20.7K]
2 years ago
7

Is -8.3 a rational number? if so can you provide it in a/b form

Mathematics
1 answer:
zalisa [80]2 years ago
6 0

Answer:

yes-8.3=\frac{-83}{10}\\is ~of ~the ~form ~\frac{a}{b}  ~where ~a=-83, ~b=10

Step-by-step explanation:

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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
Allushta [10]

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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2 years ago
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Answer:

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Step-by-step explanation:

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The figure on the left side shows the water level is at the 0.5 liter mark, ie half a liter.

1 liter = 1000 mL

0.5*1 liter = 0.5*1000 mL

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If you poured all the water into the jug on the right (without spilling), then the water level should reach the 500 mL mark. This is the small tickmark exactly halfway between the 400 and 600.

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He worked 9 hours in his first job and 5 hours in his second
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Marcus bought a phone on sale that was discounted 1/6 the
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Step-by-step explanation:

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