A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along
2 answers:
Approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.
<h3>What is Pythagoras theorem?</h3>Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
A 15-meter by 23-meter garden is divided into two sections. In this rectangle,
- Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section.
- The length of the top and bottom sides is 23 meters.
- The length of the left and right sides is 15 meters.
Here, a vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. The length of the left side of the square will be 15 long. Thus, the lenght of its diagonal is,
The length of the sidewalk in smaller rectangle in the right side of figure is,
Sum of the lengths of the two sidewalks using the pythagoras theorem is,
Thus, approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.
Learn more about the Pythagoras theorem here;
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Hi there!
We can calculate dy/dx using implicit differentiation:
xy + y² = 6
Differentiate both sides. Remember to use the Product Rule for the "xy" term:
(1)y + x(dy/dx) + 2y(dy/dx) = 0
Move y to the opposite side:
x(dy/dx) + 2y(dy/dx) = -y
Factor out dy/dx:
dy/dx(x + 2y) = -y
Divide both sides by x + 2y:
dy/dx = -y/x + 2y
We need both x and y to find dy/dx, so plug in the given value of x into the original equation:
-1(y) + y² = 6
-y + y² = 6
y² - y - 6 = 0
(y - 3)(y + 2) = 0
Thus, y = -2 and 3.
We can calculate dy/dx at each point:
At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.
At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.