Since this parabola intersects the center, its formula is:
y = ax². Given that it opens downward, the coefficient a must be negative.
Thus, the equation can be expressed as:
y = - ax², with the axis of symmetry located at x = 0.
The height measures 84 ft when the parabola's opening is 42 ft wide.
This indicates that for the height y, the corresponding x-values are +21 and -21 (due to symmetry).
To find a, let's substitute y and x with their respective values:
y = - ax²
84 = - a(21)²
84 = - a(441), leading to a = - 84/441 ↔ a = - 4/21.
Therefore, the final equation is: y = -4/21 x².
Answer:
Two thirds of a straight angle is 120°
Explanation:
First, we define a straight angle:
A straight angle measures 180°
Now, we need to find two thirds of that straight angle
To compute the fraction, multiply the straight angle's measurement by 
Thus:
of a straight angle = 
degrees
Hope this helps:)
Let's apply the Pythagorean theorem to determine whether a triangle could be formed.
Assuming we have two wooden dowels each measuring 8 inches, we can break one dowel in half, resulting in two pieces of 4 inches each.
Now we have three wooden dowels with lengths of 4 inches, 4 inches, and 8 inches.
According to the Pythagorean theorem:
a² + b² = c²
4² + 4² = 8²
16 + 16 = 64
34 ≠ 64
To form a triangle, the length of the cut wooden dowel needs to exceed that of the uncut dowel.
I also visually attempted this exercise on paper, cutting according to the assumed dimensions. No triangle can be constructed with these pieces.
Answer:
Given:
In the rhombus QRST, diagonals QS and RT cross at points W and U ∈ QR, while point V ∈ RT is such that UV⊥QR. (as illustrated in the diagram below)
To prove: QW•UR = WT•UV
Proof:
In a rhombus, the diagonals meet at right angles and bisect one another,
Thus, in QRST
QW≅WS, WR ≅ WT, and ∠QWR = ∠QWT = ∠RWS = ∠TWS = 90°.
Considering triangles QWR and UVR,
(Right angles)
(Shared angles)
By the AA similarity postulate,
The sides corresponding in similar triangles maintain proportionality,
(∵ WR ≅ WT )
Thus, it is proved.
