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Semmy [17]
3 years ago
14

Enter the number of complex zeros for the polynomial function in the box.

Mathematics
1 answer:
Finger [1]3 years ago
3 0

Given polynomial function:

f(x)=x^3-96x^2+400.

We need to apply Descartes' rule of sign to identify the number of complex roots.

The given polynomial is f(x)=x^3-96x^2+400

Let us see the number of sign changes in f(x)

There are 2 sign changes in f(x). One from plus to minus and second from plus to minus. Hence, there 2 or 0 positive roots.

Now, let us see the number of sign changes in f(-x)

f(-x)=-x^3-96x^2+400

There are only one sign change. Hence, there will be 1 negative roots.

The degree of the polynomial is 3.

Hence, there will be exactly 3 zeros.

<em>Therefore, the possible numbers of zeros are:</em>

<em>2 positive, 1 negative and 0 complex</em>

<em>0 positive, 1 negative and 2 complex.</em>

Let us see the graph:

In the graph, we can see that the graph cuts the x axis at three points (2 positive, 1 negative points).

<h3>Hence, the number of complex zeros for the given polynomial is zero.</h3>

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AnnZ [28]
  <span>Acceleration of a passenger is centripetal acceleration, since the Ferris wheel is assumed at uniform speed: 
a = omega^2*r 

omega and r in terms of given data: 
omega = 2*Pi/T 
r = d/2 

Thus: 
a = 2*Pi^2*d/T^2 

What forces cause this acceleration for the passenger, at either top or bottom? 

At top (acceleration is downward): 
Weight (m*g): downward 
Normal force (Ntop): upward 

Thus Newton's 2nd law reads: 
m*g - Ntop = m*a 

At top (acceleration is upward): 
Weight (m*g): downward 
Normal force (Nbottom): upward 

Thus Newton's 2nd law reads: 
Nbottom - m*g = m*a 

Solve for normal forces in both cases. Normal force is apparent weight, the weight that the passenger thinks is her weight when measuring by any method in the gondola reference frame: 
Ntop = m*(g - a) 
Nbottom = m*(g + a) 


Substitute a: 
Ntop = m*(g - 2*Pi^2*d/T^2) 
Nbottom = m*(g + 2*Pi^2*d/T^2) 

We are interested in the ratio of weight (gondola reference frame weight to weight when on the ground): 
Ntop/(m*g) = m*(g - 2*Pi^2*d/T^2)/(m*g) 
Nbottom/(m*g) = m*(g + 2*Pi^2*d/T^2)/(m*g) 

Simplify: 
Ntop/(m*g) = 1 - 2*Pi^2*d/(g*T^2) 
Nbottom/(m*g) = 1 + 2*Pi^2*d/(g*T^2) 

Data: 
d:=22 m; T:=12.5 sec; g:=9.8 N/kg; 

Results: 
Ntop/(m*g) = 71.64%...she feels "light" 
Nbottom/(m*g) = 128.4%...she feels "heavy"</span>
7 0
3 years ago
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7nadin3 [17]
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2 years ago
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aleksandr82 [10.1K]

Answer:

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Step-by-step explanation:

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Hope am correct

Thanks

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Answer:

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Step-by-step explanation:

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I need help with the question pictured.​
Anna35 [415]
The correct answer would be option number 2
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3 years ago
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