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WITCHER [35]
2 years ago
12

Find the distance between the two points~A ( 7 , 4 ) and B ( 3 , 2 )thankyou!​

Mathematics
2 answers:
Harman [31]2 years ago
8 0

Answer:

distance =  \sqrt{(3 - 7) ^{2} }  + (2 - 4) ^{2}  \\  =  \:  \:  \sqrt{16}  + 4 \\  \\  =  \:  \:  \:  \:   2 \sqrt{5}

vodka [1.7K]2 years ago
6 0

Answer:

AB = \sqrt{20}

Step-by-step explanation:

calculate the distance using the distance formula

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = B (3, 2 ) and (x₂, y₂ ) = A (7, 4 )

AB = \sqrt{(7-3)^2+(4-2)^2}

     = \sqrt{4^2+2^2}

     = \sqrt{16+4}

     = \sqrt{20}

     ≈ 4.47 ( to 2 dec. places )

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Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph
Dennis_Churaev [7]

ANSWER TO QUESTION 1


f(x)=(x-2)(x+3)(x-1)^2.



EXPLANATION


The function given to us is,


f(x)=x^4-x^3-7x^2+13x-6


According to rational roots theorem,


\pm1,\pm2,\pm3,\pm6 are possible rational zeros of  


f(x)=x^4-x^3-7x^2+13x-6.


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f(-3)=6-6



f(-3)=0


Also




f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6



f(2)=16-8-28+26-6



f(2)=6-6



f(2)=0


This implies that  


x-2 and x+3 are factors of



f(x)=x^4-x^3-7x^2+13x-6 and hence (x-2)(x+3)=x^2+x-6 is also a factor.



We perform the long division as shown in the diagram.



Hence,


f(x)=(x-2)(x+3)(x-1)^2.


ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots  

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Also the root x=1 has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.



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-3\le x \le 1


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f(1.5)=-0.56\:



x \ge 2



f(3)=24\:>0



We can now use these information to sketch the function as shown in diagram



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