What is the best estimate of the area of the lake pictured on the grid if each square has a side length of 400 meters?

Mathematics

1 answer:

evablogger [386]2 years ago

7 0

Answer: 4,840,000 square meters

Step-by-step explanation:

Each square has an area of (400m)^2 or 160,000 m^2 each square.

There are 390 squares, so:

(30 squares)*(160,000 m^2/square) = 4,800,000 m^2

4,840,000 square meters comes closest

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812,000 gallons of water in an olympic training center's pool. express this number in scientific notation.

frez [133]

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2 years ago

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Determine the area of the given region under the curve (1/x^4) [1,2]

Nikolay [14]

Answer:

$\displaystyle \frac{7}{24}$

General Formulas and Concepts:

Algebra I

Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

[Area] Limits of Riemann's Sums - Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Step-by-step explanation:

Step 1: Define

$\displaystyle f(x) = \frac{1}{x^4} \\ \ [1, 2]$

Step 2: Find Area

[Integral] Set up area: $\displaystyle \int\limits^2_1 {\frac{1}{x^4}} \, dx$
[Integral] Rewrite: $\displaystyle \int\limits^2_1 {x^{-4}} \, dx$
[Integral] Reverse Power Rule: $\displaystyle \frac{-1}{3x^3} \bigg| \limits^2_1$
[Area] Fundamental Theorem of Calculus: $\displaystyle \frac{7}{24}$