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barxatty [35]
3 years ago
5

Find the value of kk for which the constant function x(t)=kx(t)=k is a solution of the differential equation 3t3dxdt+5x−3=03t3dx

dt+5x−3=0.
Mathematics
1 answer:
Dafna11 [192]3 years ago
7 0
If x(t)=k is constant, then \dfrac{\mathrm dx}{\mathrm dt}=0, so you have

5k-3=0\implies k=\dfrac35
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Step-by-step explanation:

The volume of a rectangular prism is simply the product of its three dimensions: in your case, the volume of the prism is, given  

x

,

(

x

+

6

)

(

x

−

2

)

(

x

−

1

)

.

A polynomial is a sum (with some coefficients) of powers of  

x

, so, if we expand the product just written, we have

(

(

x

+

6

)

(

x

−

2

)

)

(

x

−

1

)

=

(

x

2

−

2

x

+

6

x

−

12

)

(

x

−

1

)

=

(

x

2

+

4

x

−

12

)

(

x

−

1

)

=

x

3

+

4

x

2

−

12

x

−

x

2

−

4

x

+

12

=

x

3

+

3

x

2

−

16

x

+

12

Which is a polynomial, and expresses the volume of the prism

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