The equation 2x^2+12x=4 is written in the form of 2(x-p)^2+q=0. what is the value of q?

Mathematics

1 answer:

hram777 [196]2 years ago

7 0

1) Factor out the coefficient 2: 2x^2+12x=4 => 2(x^2 + 6x) = 4

2) Complete the square of x^2 + 6x: x^2 + 6x + 9 - 9. Then:

2(x^2 + 6x + 9 - 9) = 4

3) Rewrite the square as the square of a binomial:

2( [x+3]^2 - 9) = 4, or

2([x+3]^2) = 22, or

2( [x+3]^2 ) - 22 = 0

The value of q is -22.

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aleksandr82 [10.1K]

Convert the cm to feet for the base and the height:

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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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