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Answer:
<h2>16kg</h2>
Step-by-step explanation:
This problem is borers on elasticity of materials.
according to Hooke's law,<em> "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."</em>
where F is the applied force in N
k is the spring constant N/m
e is the extension in meters
Given data
mass m= 24kg
extensnion=15cm in meters= 
= 
we can solve for the spring constant k
we also know that the force F = mg
assuming 
therefore
We can use this value of k to solve for the mass that will cause an extension of 
The answer is 42.4 because I times it: 5.3 * 18 = 95.39
Answer:
Depends on the data
Step-by-step explanation:
You need to arrange all of the data from the chart in numerical order.
Then figure out which number/numbers are in the middle of the data line.
If it was just one number that is the median. If two numbers were in the middle add them together then divide by two, that is your median.
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
