The larger of the two positive numbers is 8 more than the smaller. The sum of their squares is 104. Find the two numbers.

Mathematics

1 answer:

poizon [28]3 years ago

4 0

Hey there!

Let's set up a system of equations to find our answer. We will use x and y, with y being the larger 1.

y=x+8

x²+y²=104

We plug our value for y into the second equation and we get that y is equal to two. We can then plug this into the first equation and we get 10.

Our two numbers are two and ten.

I hope this helps!

Let's plug our y value into the second equation.

x²+x²+64=104

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By Euler's method the numerical approximate solution of the definite 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 definite integral. Euler's method is a multi-step method, related to Runge-Kutta methods, used to estimate integral 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 numerical approximation of the definite integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the numerical approximate solution of the definite integral is 4.189 648.

To learn more on Euler's method: brainly.com/question/16807646

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