Gabriella needs a mason and must decide between 2 companies. For a service visit, Company A charges $65 to send a mason plus $30
/h. Company B charges $30
to send a mason plus $47.50/h. The graph that models this situation is shown here.
According to the graph, how many hours must the two masons work in order to charge the same amount of money?
_____ hour(s)
to send a mason plus $47.50/h. The graph that models this situation is shown here.
According to the graph, how many hours must the two masons work in order to charge the same amount of money?
_____ hour(s)
2 answers:
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Answer: A. Factor 2 => 4x greater
Factor 3 => 9x greater
Factor 5 => 25x greater
Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:
A = 2.π.r.h
A cylinder of radius r and height h has area:
= 2πrh
If multiply both dimensions <u>by a factor of 2</u>:
= 2.π.2r.2h
= 8πrh
Comparing to
:
=
= 4
Doubling radius and height creates a surface area of a cylinder 4 times greater.
<u>By factor 3:</u>
Comparing areas:
=
= 9
Multiplying by 3, gives an area 9 times bigger.
<u>By factor 5</u>:
Comparing:
=
= 25
The new area is 25 times greater.
B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.