Which best describes the construction of a triangle if given the segment lengths of 10 cm, 5 cm, and 4 cm?
2 answers:
Answer:
It is not possible to construct a triangle with the given side lengths.
Step-by-step explanation:
We have been given three segment lengths and we are asked to describe about the construction of a triangle with given lengths: 10 cm, 5 cm, and 4 cm.
We will use triangle inequality theorem to answer our given problem.
Triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
So let us check our given using triangle inequality theorem as:
Now check another side.
Since the sum of our given two sides is less than third side, therefore, we can not construct a triangle with our given side lengths.
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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.