Answer:
4Joules
Step-by-step explanation:
According to Hooke's law which states that extension of an elastic material is directly proportional to the applied force provide that the elastic limit is not exceeded. Mathematically,
F = ke where
F is the applied force
K is the elastic constant
e is the extension
If a spring exerts a force of 6 N when stretched 3 m beyond its natural length, its elastic constant 'k'
can be gotten using k = f/e where
F = 6N, e = 3m
K = 6N/3m
K = 2N/m
Work done on an elastic string is calculated using 1/2ke².
If the spring is stretched 2 m beyond its natural length, the work done on the spring will be;
1/2× 2× (2)²
= 4Joules
3(5z - 7) + 2(9z - 11) = 4(8z - 7) - 111
15z - 21 + 18z - 22 = 32z - 28 - 111
33z - 43 = 32z - 139
33z - 32z = -139 + 43
z = - 96
The reasons would be:
alternate interior angles
vertical angles
AAA (all angles are congruent)
Since we know that the two line segments are parallel, this means that BC is a transversal. Using that knowledge with the position of ABE and DCE, we see these are alternate interior angles.
AEB and DEC are vertical angles, since they share only a vertex.
This gives us 3 congruent angles, so the triangles must be similar.
Answer:
Step-by-step explanation:
Let be "x" the lenght of the longest side, "y" the lenght of the middle side and "z" the lenght of the shortest side.
The perimeter is:
[Equation 1]
We know that the longest side is 10 less than twice the middle side length. This can be expressed as:
[Equation 2]
And the middle side length is three less than three times the shortest side length. This is:
[Equation 3]
The steps are:
- Solve for "z" from the third equation:
[Equation 4]
- Substitute [Equation 4] into [Equation 1]
- Substitute [Equation 2] into [Equation 1]
Then:
- Solve for "y":
- Substitute this value into [Equation 2] and into [Equation 4]:
