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Vladimir [108]
3 years ago
10

The following triangles are similar. Find x.

Mathematics
1 answer:
AlladinOne [14]3 years ago
8 0

Let's use the line on the right side. In the smaller triangle, the length is 4. The same side on the bigger triangle is 12. The ratio of the smaller triangle to the bigger triangle is:

\frac{4}{12} \rightarrow 4:12

12 \div 4 = 3

To find a side length for the bigger triangle, all you need to do is multiply by 3. The same side on the smaller triangle is 5. Multiply by 3

5 \times 3 = 15

That means x = 15

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What relation is a function? - plz help -
Eduardwww [97]

Answer:

Step-by-step explanation:

A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to. ... This is a function since each element from X is related to only one element in Y.

7 0
3 years ago
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
2 years ago
A stretched spring has a length of 12 inches when a weight of 2 lbs is attached to the spring. The same spring has a length of 1
Advocard [28]
The way I figured this one out was saying that if it takes 2lbs to stretch it to 12 inches and 5lbs to stretch to 18 inches that means that 3 additional pounds = 6 inches. Therefore, each additional pound is 2 inches. We know already that with 2 lbs it was 12 inches in length and we can also say that 2 lbs = 4 inches. So subtract 4 from 12 and you end up with the answer of 8 inches. 
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2 years ago
What two numbers plus 35 equal 180
Andrews [41]
X^2+35=180?
Subtract 35 on each side

x^2=145
Take the square root

x= -sqrt(145)
+sqrt 145...

I hope this helps!!
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Answer:

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2 years ago
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