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aivan3 [116]
2 years ago
14

Two lines, a and b, are parallel. If both of the lines aee rotated 90⁰ in the same direction and then translated to the right by

the same number of units, which statement about the lines resulting from these transformation is true?
They will be parallel.

They will be the same line.

They will be perpendicular.

They will intersect, but they won't be perpendicular.​
Mathematics
1 answer:
V125BC [204]2 years ago
5 0

Answer:

Option A

Step-by-step explanation:

The two lines if rotated by 90 degree in the same direction will remain parallel. They may become perpendicular if only one of them is rotated or will be the same line if rotated in opposite direction by same amount.

Now if these two are translated by same number of degree even then they will remain parallel. They may not remain parallel if they are translated by different angle

Hence, option A is correct

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On a snow day, Mason created two snowmen in his backyard. Snowman A was built to a height of 51 inches and Snowman B was built t
mr_godi [17]

Answer:

A ( t ) = -4t + 51

B ( t ) = -2t + 29

t < 11 hours ... [ 0 , 11 ]

Step-by-step explanation:

Given:-

- The height of snowman A, Ao = 51 in

- The height of snowman B, Bo = 29 in

Solution:-

- The day Mason made two snowmans ( A and B ) with their respective heights ( A(t) and B(t) ) will be considered as the initial value of the following ordinary differential equation.

- To construct two first order Linear ODEs we will consider the rate of change in heights of each snowman from the following day.

- The rate of change of snowman A's height  ( A ) is:

                           \frac{d h_a}{dt} = -4

- The rate of change of snowman B's height ( B ) is:

                           \frac{d h_b}{dt} = -2

Where,

                   t: The time in hours from the start of melting process.

- We will separate the variables and integrate both of the ODEs as follows:

                            \int {} \, dA=  -4 * \int {} \, dt + c\\\\A ( t ) = -4t + c

                            \int {} \, dB=  -2 * \int {} \, dt + c\\\\B ( t ) = -2t + c

- Evaluate the constant of integration ( c ) for each solution to ODE using the initial values given: A ( 0 ) = Ao = 51 in and B ( 0 ) = Bo = 29 in:

                            A ( 0 ) = -4(0) + c = 51\\\\c = 51

                           B ( 0 ) = -2(0) + c = 29\\\\c = 29

- The solution to the differential equations are as follows:

                          A ( t ) = -4t + 51

                          B ( t ) = -2t + 29

- To determine the time domain over which the snowman A height A ( t ) is greater than snowman B height B ( t ). We will set up an inequality as follows:

 

                              A ( t ) > B ( t )

                          -4t + 51 > -2t + 29

                                  2t < 22

                               t < 11 hours

- The time domain over which snowman A' height is greater than snowman B' height is given by the following notation:

Answer:                     [ 0 , 11 ]

   

8 0
3 years ago
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