2/3 is greater than, less than it equal to 5/8
2 answers:
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Answer:
Number of ducks = 37
Number of pigs = 18
Step-by-step explanation:
Let,
x be the number of ducks
y be the number of pigs
According to given statement;
x+y=55 Eqn 1
2x+4y=146 Eqn 2 (As ducks will have 2 legs and pigs will have 4)
Multiplying Eqn 1 by 2
2(x+y=55)
2x+2y=110 Eqn 3
Subtracting Eqn 3 from Eqn 2
(2x+4y)-(2x+2y)=146-110
2x+4y-2x-2y=36
2y=36
Dividing both sides by 2
Putting y=18 in Eqn 1
x+18=55
x = 55-18
x = 37
Hence,
Number of ducks = 37
Number of pigs = 18
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
<h3>How to estimate a definite integral by numerical methods</h3>In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:
∫ f(x) dx = F(b) - F(a) (1)
The steps of Euler's method are summarized below:
- Define the function seen in the statement by the label f(x₀, y₀).
- Determine the different variables by the following formulas:
xₙ₊₁ = xₙ + (n + 1) · Δx (2)
yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ) (3) - Find the integral.
The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:
y(4) ≈ 4.189 648 - 0
y(4) ≈ 4.189 648
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
To learn more on Euler's method: brainly.com/question/16807646
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