I need help on this question

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

Please help I'm stuck on these 2 problems would help so much!!<br><br> Thanks!

MrRa [10]

700 - 100 =600 she spent $600 worth of monthly payments. if there is 12 months in a year then 600 ÷ 12 = 50 so she spent $50 a month.

4 0

3 years ago

Find the measure of one interior angle in each regular polygon. round your answer to the nearest 10th if necessary.

Artist 52 [7]

S = (n-2) * 180
s = (14-2) * 180
s = 2160
2160/ 14 = 154.3
The answer is A

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2 years ago

Read 2 more answers

there are 10 crates of eggs stacked in the corner. each crate of eggs holds 20 eggs. If there is only 1 broken egg in the entire

alisha [4.7K]

Answer: 5%

Step-by-step explanation: If there is one broken egg in each crate (1/20), you would change that to5%

And if there are ten crates, then you see how many eggs there a re total.

(10 × 20 = 200)

If there are 200 eggs and for every 20 eggs there is on broken one, then there will be 10 broken eggs total. or 10/200

convert the fraction to a decimal ( 10 ÷ 200 = .05)

then convert the decimal to a percent. .05 is equal to 5%

PLEAZE RATE BRAINLIEST!!!

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3 years ago

Mr. Garza's family is attending the local soccer game. He has 30 to spend on food and drinks . The cost of chips is $2 and the c

enyata [817]

Answer:

$6

Step-by-step explanation:

let x and y be the number of chip and pretzel bags respectively : 4x%2B2y%3 C=20 : if x=1 then 4%281%29%2B2y%3C=20--->{{2y<=16}}}--->y%3C=8 : if x=3 then 4%283%29%2B2y%3C=20--->{{2y<=8}}}--->y%3C=4 : so chips 1 and pretzels 8 : chips 3 and pretzels 4.

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3 years ago