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alukav5142 [94]
3 years ago
10

2. If a, b are non-zero rational numbers, and c is a non-zero irrational number, what can we say about

Mathematics
1 answer:
topjm [15]3 years ago
5 0
B lookkkdhdvdb svdbd dhd. She d. Did d. He r. He. Hebrbeue. I’m going uuuyyyyyyyywjd
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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.

6 0
3 years ago
Find the sum of the sequence 36 37 38 39 ... 109=
uysha [10]
It's an arithmetic sequence:

a_1=36;\ a_2=37;\ a_3=38;\ ...\ ;\ a_{74}=109\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\a_1=36;\ n=74;\ a_{74}=109\\\\S_{74}=\dfrac{36+109}{2}\cdot74=\dfrac{145}{2}\cdot74=72.5\cdot74=5365
8 0
3 years ago
Identify the pair of figures in which the second figure is a translation of the first figure​
Nadya [2.5K]

Answer:

The first pair of figures would be a translation.

Step-by-step explanation:

A translation is a transformation that involves the shift or slide of a figure in the coordinate plane.  This movement will only be either horizontal, vertical or a combination of both.  The second and third set of figures given include not only a shift, but a reflection and rotation as well.  The only set of figures that has been moved horizontally and/or vertically is the first set.

8 0
3 years ago
The table shows the solution to the equation |2x - 4| - 3 = 3:
dimaraw [331]

Answer:

Step 1

Step-by-step explanation:

Step one is incorrect because you need to add 3 but it subtracted.

8 0
3 years ago
(3/4)3 write as improper fraction and mixed number
matrenka [14]
15/4, 3 3/4, and 3.75
5 0
3 years ago
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