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Misha Larkins [42]
2 years ago
13

HELP I WILL GIVE BRAINLIEST!!!!

Mathematics
1 answer:
Leokris [45]2 years ago
3 0

Answer:

Step-by-step explanation:

Solution in the attachment box

Draw the triangles it is important

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Consider the parabola r​(t)equalsleft angle at squared plus 1 comma t right angle​, for minusinfinityless thantless thaninfinity
kodGreya [7K]

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>=

                                              =2a^2t^3+2at+t

2a^2t^3+2at+t=0

take t common in above equation we get,

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

⇒t=0 or 2a^2t^2+2a+1=0

To find the solution for t;

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

The numberD = b^2 -4ac determined from the coefficients of the equation ax^2 + bx + c = 0.

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>




                                               




6 0
3 years ago
Help with question 4 please
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Answer:     y=5                           x=11

abc=def                                      

ab=de                                         <b=<e

17y-8=12+13y                              11x-4=117

-13y        -13y                                  +4   +4

4y-8=12                                      11/11x=121/11

  +8  +8                                           x=11

4/4y=20/4

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7 0
3 years ago
A polyhedron with one pentagonal base is a
alekssr [168]
I think it is an apex
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3 years ago
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What is 35.7 divided by 0.07 ?
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Answer:

35.7 / 0.07 = 510

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explanation-

I don't know how to explain but it's right!

7 0
3 years ago
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