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Roman55 [17]
3 years ago
7

Julio's father is 4 times as old as Julio. The sum of their ages is no less than 55.

Mathematics
1 answer:
seropon [69]3 years ago
8 0
Call (F) the age of the father and (J) the age of Julio

The F & J are related in this way: F=4J

 Now you have a restriction in the form of inequality: The sum of both ages has to be greater or equal than 55.

Algebraically that is: F + J ≥ 55

You can substitute F with 4J to find the solution for J: 

4J + J ≥ 55

5J ≥ 55

Now divide both sides by 5

5J/5 ≥ 55/5

J ≥ 11 

That Imposes a lower boundary for the value of J of 11, meaning that the youngest age of Julio can be 11
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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:

  1. Define the function seen in the statement by the label f(x₀, y₀).
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    xₙ₊₁ = xₙ + (n + 1) · Δx     (2)
    yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ)     (3)
  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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