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
9514 1404 393
Answer:
∛188 ≈ 5.72865
Step-by-step explanation:
Any scientific or graphing calculator or spreadsheet can tell you the cube root of 188.
∛188 ≈ 5.72865431598...
__
You know that 5³ = 125 and 6³ = 216, so the root will lie between 5 and 6, closer to 6. As a first approximation, you can figure it is about ...
x = ∛188 ≈ 5 + (188-5³)/(6³ -5³) = 5 + 63/89 ≈ 5.71
You can figure this much using a 4-function calculator.
A closer approximation (x') can be had using the iteration formula ...
x' = (2x³ +188)/(3x²)
For x = 5.71, the value of x' is ...
x' ≈ (2×5.71³ +188)/(3×5.71²) ≈ 560.3388/97.8123 ≈ 5.7287
This value is correct when the root is rounded to 4 decimal places. Another execution of the iteration formula using this value will give the root accurate to 9 decimal places.
Answer: he needs to buy 578.5 yard² of Sod.
Step-by-step explanation:
Assuming the lawn is square shaped, the formula for determining the area of a square is
Area = length²
If the length of each side of the lawn is 24 1/2 = 24.5 ft
Area of the lawn = 24.5² = 600.25yard²
The area of the pool house is 16yard²
The area of the side walk is
3 × 1 = 3 yard²
The length of the pool is 7 1/2 = 7.5yards
The width of the pool is 2 1/2 = 2.5 yards. Therefore,
Area of pool = 7.5 × 2.5 = 18.75 yard²
Therefore, the amount of Sod that he needs to buy is
600.25 - (3 + 18.75) = 600.25 - 21.75
= 578.5 yard²
