Clark has 7 and 1 over 2 feet of wire.
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The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.
<h3>How to determine the approximate area of the regions bounded by the curves</h3>
In this problem we must use definite integrals to determine the area of the region bounded by the curves. Based on all the information given by the graph attached below, the area can be defined in accordance with this formula:
A = A₁ + A₂ (1)
A₁ = ∫ [g(x) - f(x)] dx, for x ∈ [- 0.786, 0] (2)
A₂ = ∫ [f(x) - g(x)] dx, for x ∈ [0, 1.151] (3)
g(x) = x⁴ - x (4)
f(x) = x / √(x² + 1) (5)
Then, we proceed to find the integrals:
∫ g(x) dx = ∫ x⁴ dx - ∫ x dx = (1 / 5) · x⁵ - (1 / 2) · x² (6)
∫ f(x) dx = ∫ [x / √(x² + 1)] dx = (1 / 2) ∫ [2 · x / √(x² + 1)] dx = (1 / 2) ∫ [du / √u] = √u = √(x² + 1) (7)
And the complete expression for the integral is:
A = A₁ + A₂ (1b)
A₁ = (1 / 5) · x⁵ - (1 / 2) · x² - √(x² + 1), for x ∈ [- 0.786, 0] (2b)
A₂ = √(x² + 1) - (1 / 5) · x⁵ + (1 / 2) · x², for x ∈ [0, 1.151] (3b)
A₁ = 0.023
A₂ = 0.783
A = 0.023 + 0.783
A = 0.806
The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.
To learn more on definite integral: brainly.com/question/14279102
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Answer:
The interquartile range of the data set is: 11 years
Step-by-step explanation:
The ages of a group of state governors at their inaugurations are listed below :
50,38,45,47,53,54,57,40,57,64,58,52
On arranging our data in increasing order i.e. in ascending order we have:
38 40 45 47 50 52 53 54 57 57 58 64
we divide our data into quartiles.
- The median of the data i.e.
is the middle value of the set.
Here in thus data the middle value will lie between 52 and 53.
Hence, the median is
- the lower data is given as:
38 40 45 47 50 52
Hence will lie between 45 and 47 which is 46.
Hence,
- the upper data is given as:
53 54 57 57 58 64
Hence, will lie between 57 and 57 which is 57.
Hence,
Hence, the interquartile range of the data is given as:
.
Hence, the interquartile range is 11 years.