When we divide the interval from 1 to 5 into 4 subintervals, each has a width of 1. Simpson's rule has us evaluate the integral as
... integral = (1/3)(f(1) +4f(2) +2f(3) +4f(4) +f(5)) = (1/3)(10 +4·25 +2·46 +4·73 +106)
... integral = (1/3)(600) = 200 . . . . . by Simpson's rule
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The integral evaluates to
![\displaystyle \int_{1}^{5}{\left(3x^2+6x+1\right)}\,dx=\left[x^3+3x^2+x\right]\limits_{1}^{5}=(5^3-1^3)+3(5^2-1^2)+(5-1)\\=124+3*24+4=200](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B1%7D%5E%7B5%7D%7B%5Cleft%283x%5E2%2B6x%2B1%5Cright%29%7D%5C%2Cdx%3D%5Cleft%5Bx%5E3%2B3x%5E2%2Bx%5Cright%5D%5Climits_%7B1%7D%5E%7B5%7D%3D%285%5E3-1%5E3%29%2B3%285%5E2-1%5E2%29%2B%285-1%29%5C%5C%3D124%2B3%2A24%2B4%3D200)
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Simpson's rule uses a quadratic interpolation, so evaluates quadratics exactly.
Answer:
- 740 meters of fence
- 22,000 square meters
Step-by-step explanation:
Two of the sides total 150 +220 = 370 meters. The other two sides are the same lengths, so the sum of lengths of the four sides is ...
2·370 m = 740 m . . . . . length of fence needed
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The area of a parallelogram is the product of base and height.
A = bh = (220 m)(100 m) = 22,000 m^2 . . . . area the fence encloses
Answer:
y = 30x
Step-by-step explanation:
y is the amount of money
30 is the constant, the amount of money she gets per x, month
To find the volume of a dome, you would have to find the volume of the sphere, theoretically, and then divide it by two. To calculate the volume, we would use the formula 4/3
. The radius (r) in this case is half of the diameter which is 14. 4 x 3.14 (pi) = 12.56. 12.56 x 14 x 14 x 14 (2744) = 34464.64. If we divide this number by 3, we get 11488.2133. If we divide this by 2 (to get the dome), we get 5744.10656. Which would be 5744.1 rounded to the nearest tenth.
