The diagram shows a circular pond, of radius r metres, surrounded by a circular path.The circular path has a constant width of 1
1 answer:
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
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Using the midpoint formula, the coordinates of endpoint H are (4, -6).
<h3>The Midpoint Formula</h3>The midpoint formula is given as:
<em>Where</em>,
= coordinates of the midpoint
= coordinates of the first point
= coordinates of the second point
Given the following:
= M( 6,-4)
= G(8,-2)
= H(?, ?)
Plug in the values into the midpoint formula
Solve for the x-coordinate and y-coordinate separately
- Multiply both sides
Therefore, using the midpoint formula, the coordinates of endpoint H are (4, -6).
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