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melomori [17]
3 years ago
15

Plz help! what is the end of behavior of f(x)?

Mathematics
1 answer:
Tanzania [10]3 years ago
5 0

Answer:

B

Step-by-step explanation:

The end behavior of a function is how the graph behaves as it approaches negative and positive infinity.

Let's take a look at each end.

As x approaches negative infinity:

As x approaches the left towards negative infinity, we can see that the graph is shooting straight upwards.

Therefore, as x\rightarrow-\infty, our function f(x) is increasing and increasing up towards positive infinity.

Therefore, the end behavior at the left will be:

\text{As } x\rightarrow-\infty, f(x)\rightarrow\infty

As x approaches (positive) infinity:

As x approaches the right towards positive infinity, we can see the that graph is also shooting straight upwards.

Therefore, the end behavior will be exactly the same. As x approaches positive infinity, f(x) <em>also</em> approaches positive infinity.

Therefore, the end behavior at the right will be:

\text{As } x\rightarrow \infty, f(x)\rightarrow \infty

Therefore, our answer is B.

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Answer:

A ( t ) = -4t + 51

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

Step-by-step explanation:

Given:-

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- 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.

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                           \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

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                              A ( t ) > B ( t )

                          -4t + 51 > -2t + 29

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

Answer:                     [ 0 , 11 ]

   

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