Answer:
Step-by-step explanation:
The volume of the prism is 252 cubic centimeters.
The volume of a rectangular prism is gotten by the formula:
V = l * w * h
where l = length
w = width
h = height
The height of the prism is 3 cm.
Let x be the width of the prism.
The length of the prism is 5 cm longer than the width.That is:
l = 5 + x
The volume of the prism is therefore:
V = (5 + x) * x * 3
This is the equation that models the volume of the tray in terms of x.
I think the shaded region for this problem will the part of the circle that is not covered by the triangle. First, determine the area of the circle by the equation,
A = πD²/4
Substituting the given diameter,
A = π(16 ft)²/4 = 200.96 ft²
Then, determine the area of the triangle with the equation,
A = bh/2
Since the base of the triangle is the diameter, b = 16 ft. Then, its height will be half the height and that will be equal to 8 ft. Substituting,
A = (16 ft)(8 ft) / 2 = 64 ft²
The difference between the two areas is 136.96 ft².
Answer:
Step-by-step explanation:
Use midpoint formula to find the coordinates of each midpoint.
(x, y) = (½ (x₁ + x₂), ½(y₁ + y₂))
Coordinates of D:
(x, y) = (½ (4 + 2), ½(6 + -2))
(x, y) = (3, 2)
Coordinates of E:
(x, y) = (½ (4 + -2), ½(6 + -4))
(x, y) = (1, 1)
Slope of DE:
m = Δy / Δx
m = (2 − 1) / (3 − 1)
m = 1/2
Slope of BC:
m = Δy / Δx
m = (-2 − -4) / (2 − -2)
m = 1/2
Therefore, DE is parallel to BC.
Use calculator it’s just square roots
