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Nonamiya [84]
3 years ago
13

Zuri made 2 spheres using plaster. The smaller sphere has a radius of 6 cm. The larger sphere has a radius of 24 cm.

Mathematics
1 answer:
Sliva [168]3 years ago
7 0
Since we are dealing with volume, when one object is 4 times bigger than another, the difference in volume is 4^3 = 64.

6 cm sphere = 4/3 *PI * 6^3
6 cm sphere = 4/3 *PI * 216
6 cm sphere = <span> <span> <span> 904.78 cc

24 cm sphere = </span></span></span>4/3 *PI * 24^3
24 cm sphere = 4/3 *PI * 13,824
24 cm sphere = <span> <span> <span> 57,905.84 </span> </span> </span> cc

Comparing the volumes: <span>57,905.84 / 904.78 = </span><span><span><span>64 </span>


</span> </span> <span>
</span>
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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
3(n+4)=21 what does n =?
Brilliant_brown [7]

Answer:

3.

Step-by-step explanation:

3(n + 4) = 21

3n + 12 = 21

3n = 21 - 12 = 9

n = 3.

7 0
3 years ago
Read 2 more answers
What is the perimeter of RSTUV?
MrMuchimi

Answer:

this should be 132 units   i hope this helps!   :)

Step-by-step explanation:

so these figures are similar

we are given 3 side measurements on one, and 3 on the other

we know that side BA is 10 units, and that SR which is the same side, is 14 units

we can conclude that they added 4 units to this side

so with the other side lengths that we are given we can figure out what the length of the perimeter of RSTUV is

10 + 4 = 14

15 + 4 = 19

28 - 4 = 24  

42 - 4 = 38

25 + 4 = 29

42 TU

28 UV

19 VR

14 SR

29 ST

add all the side together to get 132 units

3 0
3 years ago
18 - 2x = y
DerKrebs [107]

B. Y equals 0, because if you plug it in ( multiply 2 by 9 ) you will get 18-18 which equals 0.
6 0
3 years ago
What is the exponential form of the expanded form below?<br> 4.4.4.4.4.4
marishachu [46]
The Second Choice I think
7 0
3 years ago
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