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Anestetic [448]
2 years ago
11

In 1603, German astronomer Christoph Scheiner began to copy and scale diagrams using an instrument that came to be known as the

pantograph. By moving a pencil attached to a linkage, Scheiner was able to produce a second image that was enlarged. Do some brief research on Scheiner’s invention. Describe how the pantograph works and how it is able to produce an enlarged image. How does the operation of the pantograph relate to dilations and similarity? How can you use similar triangles to describe why the pantograph works as it does? Write an abbreviated paragraph proof using similar triangles to explain the design. In many instances, the pantograph has been replaced by other means for enlarging images. What has the pantograph been replaced by? Explain. 13 Response(s)
Mathematics
1 answer:
Softa [21]2 years ago
4 0

Answer:

1.    The pin’s location aids to create two drawings simultaneously. This is that while drawing an image, a copy, which may vary in size, is created at the same time.

2.    The pantograph relates to dilation and similarity due to the use of similar triangles that affect the scale of the second drawing.  

3.    The use of similar triangles illustrates the process of the pantograph because the ratio of similitude is set when determining where to place the pin. When a triangle is moved while tracing a line, along with the outline of the image, an enlarged/reduced version of the image is created by the other pantograph's end.

4.    The pantograph is now obsolete and has been replaced by several different ways of producing duplicates such as photocopying, mass printing, and digital filing.


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If you increase your current quality score of 85% by 7%,
svlad2 [7]
85 x 0.07 = 5.95

Total = 85 + 5.95 = 90.95%
5 0
2 years ago
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2 Rita bought three and forty-eight hundredths pounds of bananas at the store. How is this number written in expanded notation?
boyakko [2]

The cost of bananas = $ 3.48

This can be written as :                                                                                            

this number written in expanded notation as : (3 × 1) + (4 × 0.1) + (8 × 0.01)

3+0.4+0.08 = 3.48

Hence, 1st option is correct.                                                  

5 0
2 years ago
Assuming that the Chinese population continues to grow at the same rate, how many years until the population reaches 1.5 billion
faltersainse [42]

Answer:

29 years

Step-by-step explanation:

The population of the Chinese people is 1.3 bn, and they grow at a rate of 0.49% per year. To get the number of years it requires to reach 1.5 bn, we use this method

after x years, the population will be

1.3 * 1.0049^x

so you just need to solve

1.3 * 1.0049^x = 1.5

1.0049^x = 1.5/1.3

x log 1.0049 = log(1.5/1.3)

x = log(1.5/1.3)/log(1.0049)

x = 0.062 / 0.002122

x = 29.25 years

Therefore, at the rate of 0.49%, the Chinese population of 1.3bn needs 29 years to clock 1.5 bn

8 0
2 years ago
The table below shows the typical hours worked by employees at a company. A salaried employee makes $78,000 per year. Hourly emp
MrRa [10]

Given:

  • The table of typical hours worked by employees at a company
  • salaried employee makes $78,000 per year
  • hourly employees get $26 per hour and $39 per hour when they work more than 40 hours.

To Find: Which payment option to recommend to a new employee.

Solution: I would recommend being a salaried employee.

Explanation:

We begin by calculating the typical number of hours worked per week.

Adding up the hours from the table, we have 0+8+8.5+9.5+10+8+3=47.

The payment for an hourly employee must be calculated as $26 per hour for working till 40 hours, and $39 per hour when they work more than 40 hours.

So, the payment for 47 hours of work per week will be (26)(40) + (39)(7) = 1313 dollars.

As there are 52 weeks in a year, the yearly payment for an hourly emplyee would be (1313)(52) = 68276. That is, an hourly employee would earn $68276.

On the other hand, we are given that a salaried employee makes $78000 per year which is more money than what an hourly employee makes for the same amount of work.

Therefore, I would recommend a new emplyee to be paid a salary rather than work on an hourly basis.


6 0
2 years ago
Read 2 more answers
A quadratic pattern has a second term equal to 1,a third term equal to -16 and a fifth term equal to -14
chubhunter [2.5K]
Given are several terms in a quadratic pattern:

a1 = ?
a2 = 1
a3 = -16
a4 = ?
a5 = -14

let:

x       y
1       ?
2       1
3      -16
4       ?
5       -14

considering the 2nd term and 3rd term, we can determine a quadratic function:

y = -17x + 35

therefore,

a1 = 18
a4 = -33
7 0
2 years ago
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