Answer: 818.4
Step-by-step explanation:
Using the area of a sector formula, we get the area of the entire sector is 
.
Using the formula 
, we get the area of the triangle is 
.
So, the area of the shaded sector is 
It has landed on its side 25/30 times, on the top 4/30 times 25/30=5/6,1/30=0.2/6 and 4/30=0.8/6.
The amswer would be 8.5 due to the length of the obeject
The differences between the trapezoidal rule and simpson's rule is -
The trapezoidal rule and Simpson's method, the latter a set of formulas of varying complexity, are both Newton-Cotes formulas, that are used to examine and model complex curves.
<h3>What is
trapezoidal rule?</h3>
The trapezoidal rule is just an integration rule that divides a curve into small trapezoids to calculate the area under it. A area under the curve is calculated by adding the areas of all the small trapezoids.
Follow the steps below to use the trapezoidal rule to determine the area under given curve, y = f. (x).
- Step 1: Write down the total number of sub-intervals, "n," as well as the intervals "a" and "b."
- Step 2: Use the formula to determine the width of the sub-interval, h (or) x = (b - a)/n.
- Step 3: Use the obtained values to calculate this same approximate area of a given curve, ba f(x)dx Tn = (x/2) [f(x0) + 2 f(x1) + 2 f(x2) +....+ 2 f(n-1) + f(n)], where xi = a + ix
<h3>What is
Simpson's method?</h3>
Simpson's rule is used to approximate the area beneath the graph of the function f to determine the value of the a definite integral (such that, of the form b∫ₐ f(x) dx.
Simpson's 1/3 rule provides a more precise approximation. Here are the steps for using Simpson's rule to approximate the integral ba f(x) dx.
- Step 1: Figure out the values of 'a' & 'b' from interval [a, b], as well as the value of 'n,' which represents the number of subintervals.
- Step 2: Determine the width of every subinterval using the formula h = (b - a)/n.
- Step 3: Using the interval width 'h,' divide this same interval [a, b] [x₀, x₁], [x₁, x₂], [x₂, x₃], ..., [xn-2, xn-1], [xn-1, xn] into 'n' subintervals.
- Step 4: In Simpson's rule formula, substitute all of these values and simplify. b∫ₐ f(x) dx ≈ (h/3) [f(x0)+4 f(x1)+2 f(x2)+ ... +2 f(xn-2)+4 f(xn-1)+f(xn)].
Thus, sometimes we cannot solve an integral using any integration technique, and other times we don't have a particular function to integrate. Simpson's rule aids in approximating the significance of the definite integral in such cases.
To know more about the Simpson's method and trapezoidal rule, here
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The school council will have 216 small sandwiches.
Step-by-step explanation:
Sandwiches ordered = 12
Length of one sandwich = 6 feet
1 foot = 12 inch
6 feet = 12*6 = 72 inches
Length of one sandwich in inches = 72 inches
As one small sandwich is 4 inches,
Number of small sandwiches in one sandwich = 
One sandwich = 18 small sandwiches
12 sandwiches = 18*12 = 216 small sandwiches
The school council will have 216 small sandwiches.
Keywords: multiplication, division
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