Rule for the relationship between certain quantities.<br> Domain<br> Origin<br> Formula<br> Term

Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is $z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$ .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be $z (x) = \cos x$ the base formula, where $x$ is measured in sexagesimal degrees. This expression must be transformed by using the following data:

$T = 180^{\circ}$ (Period)

$z_{min} = -4$ (Minimum)

$z_{max} = 5$ (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of $2\pi$ radians. In addition, the following considerations must be taken into account for transformations:

1) $x$ must be replaced by $\frac{2\pi\cdot x}{180^{\circ}}$ . (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

$\Delta z = \frac{z_{max}-z_{min}}{2}$

$\Delta z = \frac{5+4}{2}$

$\Delta z = \frac{9}{2}$

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

$z_{m} = \frac{z_{min}+z_{max}}{2}$

$z_{m} = \frac{1}{2}$

The new function is:

$z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)$

Given that $z_{m} = \frac{1}{2}$ , $\Delta z = \frac{9}{2}$ and $T = 180^{\circ}$ , the outcome is:

$z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

8 0

3 years ago

The average monthly rainfall for 6 months was 28.5 mm. If it had rained 1mm more each month what would the average have been? By

Fynjy0 [20]

Answer:

29.5 mm

Step-by-step explanation:

We are told that the average monthly rainfall for 6 months was 28.5 mm.

Thus, total for the 6 months = 28.5 × 6 = 171 mm

Now, we are told that it rained 1 mm extra each month.

So extra for the six months = 1 × 6 = 6mm

New total for 6 months = 171 + 6 = 177 mm

So, new average for 6 months = 177/6 = 29.5 mm

4 0

3 years ago

Olivia will attend Blake University this fall. Tuition for one year is $11,350. Olivia plans to earn $1,500 at her work-study jo

g100num [7]

Answer:

4650 add 1500+1800+3400 u get 6700

then you get the tuition cost then subtract it by 6700

your final answer is 4650 dollar

8 0

3 years ago

The Jones family and the Connor family both bought the same boxed package of sugar cubes at the store, in which the cubes were a

GrogVix [38]

Answer:

180

Step-by-step explanation:

At the beggining, it says they are stacked in 5 layers which means the number of cubes is divisible by 5.

If the number of cubes equals x:

The least amount of sugar cubes the Jones family could have used is $61*2$ which equals 122. The most they couldve used is $61*3$ which equals 183.

Based on the information from the Jones family, x is between 122 and 183.

Based on the information from the Connor's, x is between 176 and 264.

Based on the information from both, x is between 176 and 183. The only number that is divisible by 5 between those numbers is 180 cubes.

3 0

2 years ago

Find the value of y 74 77 89 96

Morgarella [4.7K]

The external angle (53°) is half the difference of the intercepted arcs (y°, 180°), so we have
53 = (180 - y)/2
106 = 180 - y
y = 180 - 106
y = 74

The appropriate choice for the value of y is ...
74

4 0

3 years ago

Rule for the relationship between certain quantities. Domain Origin Formula Term