A
Given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 ), then
The x-coordinate of the vertex is
= -
y = - 3x² + 2x - 7 is in standard form
with a = - 3, b = 2 and c = - 7, hence
= -
=
Substitute this value into the equation for y-coordinate
y = - 3 ()² + 2 (
) - 7
= - +
-
= -
vertex = ( , -
) → A
Answer:
Area of the shaded region = 23.33 in²
Step-by-step explanation:
Area of a sector =
Where θ = Central angle subtended by an arc
r = radius of the circle
Area of the sector BCD =
= 52.36 in²
Area of equilateral triangle BCD =
=
= in²
= 43.30 in²
Area of the shaded portion in ΔBCD = 52.36 - 43.3
= 9.06 in²
Area of sector CAD =
= 39.27 in²
Area of right triangle CAD =
=
=
= 25 in²
Area of the shaded part in the ΔACD = 39.27 - 25
= 14.27 in²
Area of the shaded part of the figure = 9.06 + 14.27
= 23.33 in²
The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)
<h3>How to interpret Cycle Graphs?</h3>
From the diagram attached, we can say that;
Period = 2π/k
where;
k = 2π/2.25
k = 8π/9
Thus;
h(t) = -(48/2) cos (8π/9)t + ((48/2) + 0.5)
h(t) = -24cos (8π/9)t + 24.5
Riders can see Niagara falls if they are higher than 41 meters above the ground. Thus;
41 = -24cos (8π/9)t + 24.5
41 - 24.5 = -24cos (8π/9)t
16.5 = -24cos (8π/9)t
-0.6875 = cos (8π/9)t
cos⁻¹0.6875 = (8π/9)t
t = 0.834 min
Thus, time interval is between;
0.834 < t < (2.25 - 0.834)
⇒ 0.834 < t < 1.416 and
(2.25 + 0.834) < t < (2.25 + 1.416)
⇒ (3.084, 3.666)
Read more about Cycle Graphs at; brainly.com/question/24461724
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