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3 years ago

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On a scale drawing, the height of a tree is 2. 25 inches. If the scale of the drawing is 1 inch : 75 feet, how tall is the tree?

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1 answer:

Marta_Voda [28]3 years ago

5 0

Answer:

168.75

Explanation:

168.75 tall is the tree.

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Estimate 10 0 f(x) dx using five subintervals with the following.

geniusboy [140]

The value of the <em>definite</em> integral $\int\limits^{10}_{0} {f(x)} \, dx$ has an <em>approximate</em> value of 5 units.

<h3>How to estimate the area below the curve by Riemann sum</h3>

A definite integral within a given interval is represented graphically by the net area below the curve. In this question we must estimate the <em>total</em> area of the curve by <em>right</em> Riemann sum. The most accurate approximation is using Riemann sum with trapezoids, whose formula is defined below:

$A = \frac{b-a}{2\cdot n} \sum_{i=0}^{n-1} \left[f(x_{i})+f(x_{i+1})\right]$ (1)

Where:

<em>n</em> - Number of subintervals
<em>a</em> - Lower limit
<em>b</em> - Upper limit
<em>i</em> - Subinterval index

If we know that <em>n = 5</em>, <em>a = 0</em> and <em>b = 10</em>, then the area of the curve is approximately:

$A = \left[\frac{10-0}{2\cdot (5)} \right]\cdot [(f(0)+f(2))+(f(2)+f(4))+(f(4)+f(6))+(f(6)+f(8))+(f(8)+f(10))]$

$A = f(0) + 2\cdot f(2) + 2\cdot f(4) + 2\cdot f(6) + 2\cdot f(8) + f(10)$

$A \approx 3 + 2\cdot (0) + 2\cdot (-1) + 2\cdot (-2)+2\cdot (2) + 4$

$A\approx 5$

The value of the <em>definite</em> integral $\int\limits^{10}_{0} {f(x)} \, dx$ has an <em>approximate</em> value of 5 units. $\blacksquare$

<h3>Remarks</h3>

The figure of the function f(x) is missing. We include a simplified version of the image in the picture attached below. In addition, the statement is poorly formatted, correct form is shown below:

<em>Estimate </em> $\int\limits^{10}_{0} {f(x)} \, dx$ <em> using five subintervals with the following.</em>

To learn more on Riemann sums, we kindly invite to check this verified question: brainly.com/question/21847158

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