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Fittoniya [83]
3 years ago
9

What is the area of the square?* Perimeter =60m

Mathematics
1 answer:
djverab [1.8K]3 years ago
3 0

Answer:

A = 225 m ^2

Step-by-step explanation:

The perimeter of a square is found by

P =4s where s is the side of a square

60 = 4s

Divide each side by 4

60/4 =4s/4

15 = s

Now we need  to find the area

A = s^2 for the area of a square

A = 15^2

A = 225 m ^2

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Given:-   r(t)=< at^2+1,t>  ; -\infty < t< \infty , where a is any positive real number.

Consider the helix parabolic equation :  

                                              r(t)=< at^2+1,t>

now, take the derivatives we get;

                                            r{}'(t)=

As, we know that two vectors are orthogonal if their dot product is zero.

Here,  r(t) and r{}'(t)  are orthogonal i.e,   r\cdot r{}'=0

Therefore, we have ,

                                  < at^2+1,t>\cdot < 2at,1>=0

< at^2+1,t>\cdot < 2at,1>=

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t\cdot \left (2a^2t^2+2a+1\right )=0

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take 2a^2t^2+2a+1=0

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The determinant D=0-4(2a^2)(2a+1)=-8a^2\cdot(2a+1)

Since, for any positive value of a determinant is negative.

Therefore, there is no solution.

The only solution, we have t=0.

Hence, we have only one points on the parabola  r(t)=< at^2+1,t> i.e <1,0>




                                               




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