Answer:
The function is defined as H (t) = 4 cos (2π/5 ( t - 1.5)) + 8
Step-by-step explanation:
Solution
Let the function be a cosine function
H(t) a cos(b(t+c)) + d
Now,
The maximum height,is H max =12
The minimum height , is H min = 4
The amplitude, a is denoted by
:
a= H max - H min/2
= 12 - 4/2 = 8/2 = 4
Thus,
The vertical shift , d is given by:
d = H max + H min/2
= 12 + 4 /2 = 16/2 = 8
The period T is given by,
T=6.5-1.5=5
So,
b is given by ,
b= 2π /T = 2π/5
The phase shift , c is given by
:
since maximum height occur at 1.5 we get, c=-1.5
Therefore, our function is defined as:
H (t) = 4 cos (2π/5 ( t - 1.5)) + 8
The one that does not belong is plane CDE, the reason being the rest are line segments. Line segments differ from the planes because they have fewer number of dimensions as compared to the planes. Thus the correct answer is:
plane CDE
reason being:
The one that does not belong has different number of dimensions
Given:
Vertex 1 (-2,-3)
Vertex 2 (3,5)
Vertex 3 (8,-1)
Reflection across the x-axis rule (x,y) → (x -y)
Vertex 1 (-2,-3) → (-2,-(-3)) → (-2,3)
Vertex 2 (3,5) → (3,-5)
Vertex 3 (8,-1) → (8,-(-1)) → (8,1)
Rotation 90° clockwise (x,y) → (y,-x) *I'm assuming the original triangle was rotated and not the reflection.
Vertex 1 (-2,-3) → (-3,-(-2)) → (-3,2)
Vertex 2 (3,5) → (5,-3)
Vertex 3 (8,-1) → (-1,-8)
