Which transformations are needed to change the parent cosine function to the cosine function below?
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
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
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
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

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

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

-2/

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204