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irina [24]
3 years ago
14

I need help on this question

Mathematics
1 answer:
poizon [28]3 years ago
8 0

Can you take picture better?I need to see this good

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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
4 0
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!!!

3 0
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.

4 0
3 years ago
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