The formula for calculating the area of a circle is expressed as;
A = πr²
- Area of the pond = πr²
- Area of the path = Area of the path + pond - area of pond
- Area of path = π(r+1.5)² - πr²
Since the area of the path is equal to the area of the pond, hence;
π(r+1.5)² - πr² = πr²
Add πr² to both sides
π(r+1.5)² - πr² + πr² = πr² + πr²
π(r+1.5)² = 2πr²
(r+1.5)² = 2r²
Expand the parenthesis
r²+3r + 2.25 = 2r²
r²+3r + 2.25 - 2r² = 0
-r² + 3r + 2.25 = 0
r² - 3r - 2.25 = 0
Multiply through by 2
2r² - 6.0r - 4.5 = 0
<em>This proves the required equation</em>
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Learn more on area of composite figures here: brainly.com/question/15981553
The striped rectangle has a total area of 69,375 cm².
<h3>How to calculate the area of the
striped rectangle?</h3>
To find the area of the striped rectangle we must carry out the following procedures.
Find the area of each segment of the rectangle, that is, what is the area of each of the 24 squares that make up the rectangle, for that we divide the 111cm² of the total area into 24.
According to the above, we infer that each square has an area of 4.625cm².
On the other hand, to find the area of the striped rectangle we must take into account that it is 5 squares long by 3 squares high, that is, its area is 15 squares.
Finally, each square has an area of 4.625cm², so to find the total area of the striped area we must multiply the area of each square by the number of squares.
15 × 4.625cm² = 69.375cm²
Learn more about areas in: brainly.com/question/27683633
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Answer:
Yes. Intergers are all whole numbers so negative whole numbers are included too.
Step-by-step explanation:
Answer:
To the nearest hundredth, this is 30.79 units
Step-by-step explanation:
To find the length of the arc, we simply apply the length of arc formula
Mathematically, that would be;
theta/360 * 2 * pi * r
Theta here is 98
r is 18 units
So the length of the arc will be;
98/360 * 2 * 22/7 * 18
= 30.7876 units
to the nearest hundredth, this is;
30.79 units