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brilliants [131]
3 years ago
10

Please Help, 20 points and brainiliest, URGENT.

Mathematics
1 answer:
ch4aika [34]3 years ago
4 0

Answer:

Step-by-step explanation:

∠ACB and ∠ECD are vertical angles, so ∠ACB = ∠ECD.

∠D = ∠B

∠A = ∠E

△ABC and △EDC are similar because they have the same angles.

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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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