A walking path at a local park is modeled on the grid below where the length of each grid square is 10 feet. The town needs to s
ubmit paperwork to pave the walking path. Determine and state, to the nearest square foot, the area of the walking path.
1 answer:
Answer:
The area of the walking path = 3,371 ft²
Explanation:
The complete Question is presented in the attached image to this solution
Note that the walking path consists of straight paths and curved paths.
The straight path is strictly squares, with 9 of them on both sides (top and bottom)
Area of the straight path = 18 × area of one square = 18 × 10² = 1800 ft²
For the curved path, note that their areas is the area between two semi circles.
Smaller semicircle has a radius of r = 20 ft.
Larger semicircle has a radius of R = 30 ft.
Area between the two semicircles = (Area of larger semicircle) - (Area of smaller semicircle)
= (πR²/2) - (πr²/2)
= (π×30²/2) - (π×20²/2)
= 785.4 ft²
But note that there are two of those curved paths, hence, area of the curved paths
= 2 × 785.4 = 1570.8 ft²
Total area of the walking path = (Area of straight path) + (Area of curved path)
= 1800 + 1570.8 = 3370.8 ft² = 3371 ft² to the nearest whole number.
Hope this Helps!!!
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Answer:
Number of units possible in S are 4.
Explanation:
Given <em>S</em> is a set of complex number of the form where <em>a</em> and <em>b</em> are integers.
is a unit if
exists such that
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Number of units possible = ?
Solution:
Given that:
Taking modulus both sides:
Using the property that modulus of product of two complex numbers is equal to their individual modulus multiplied.
i.e.
So,
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Let
Then modulus of z is
Given that a and b are <em>integers</em>, so the equation (1) can be true only when (Reciprocal of 1 is 1). Modulus can be equal only when one of the following is satisfied:
(a = 1, b = 0) , (a = -1, b = 0), (a = 0, b = 1) OR (a = 0, b = -1)
So, the possible complex numbers can be:
Hence, number of units possible in S are 4.