I think it would be The first term indicates that the 14 girl scouts each sold 22 boxes of cookies per additional day of the fair. The second term indicates that the 14 girl scouts each sold 25 boxes of cookies on the first day of the fair.
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.
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The amount needed to purchase materials needed to cover the area of the triangular flag is: $54.
<h3>What is the Area of a Triangle?</h3>
Area of a triangle = 1/2(bh)
Given the dimensions of the flag as the following:
base (b) = 18 in.
height (h) = √(41² - 9²) = 40 in.
Area of the flag = 1/2(18)(40) = 360 in.²
Cost of material needed = (360)(0.15) = $54
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Answer:
angle GKF because they are vertically opposite angle