Fourth term of sequence is 216, sixth term 96
1 answer:
You might be interested in
Question:
1. vertical stretch of 2, horizontal stretch to a period of 2 pi, phase shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of 1 unit up
2. vertical compression of 2, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of 2 units down
3. vertical compression of 2, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of 1 unit down
4. vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down
Answer:
The correct option is;
4. Vertical stretch of 2, horizontal compression to a period of π/2, phase shift of π units to the right, vertical shift of 1 unit down
Step-by-step explanation:
Here, we have the parent cosine function given by y = cos(x)
A plot of the above function is attached
By comparison, it is observed that the transformation required to change the parent function includes;
1. Vertical stretch from the parent function of amplitude 1 to amplitude 2
2. A horizontal compression so that the period of one complete revolution is π/2 rather than 2·π in the parent cosine function
3. Phase shift of pi units to the right such that cos(π) = 1 rather than cos(2π) = 1 as it applies to the parent function
4. Shift of the y values from the symmetrical x-axis origin downwards by 1 unit such that the maximum y value of the doubly stretched transformation is 1 rather than 2
For x-intercepts "b" and "c", a quadratic can be written as
y = a(x -b)(x -c)
You know the x-intercepts, so you can write the equation as
y = a(x +2)(x -3) . . . . . . eliminates the first two answer choices
Substituting (x, y) = (-1, 2), you have
2 = a(-1+2)(-1-3) = -4a
Then dividing by -4 gives
-2/4 = a = -1/2 . . . . . corresponds to the third answer choice
The appropriate selection is
y = -1/2 (x + 2)(x - 3)
y = a(x -b)(x -c)
You know the x-intercepts, so you can write the equation as
y = a(x +2)(x -3) . . . . . . eliminates the first two answer choices
Substituting (x, y) = (-1, 2), you have
2 = a(-1+2)(-1-3) = -4a
Then dividing by -4 gives
-2/4 = a = -1/2 . . . . . corresponds to the third answer choice
The appropriate selection is
y = -1/2 (x + 2)(x - 3)
SSS theorem: If two triangles have three pairs of sides in the same ratio, then the triangles are similar.
Write the ratio between the smallest sides, between the greatest sides and between the middle sides and compare the results:
This gives you that
By SSS theorem triangles ABC and EFG are similar with scale factor 180.