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anonymous

  • 5 years ago

The parametric representation r(s,t)=2tcos(s)i + 2tsin(s)j + tk for s∈R and t∈R corresponds to what surface? What is mean by s∈R and t∈R?

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  1. anonymous
    • 5 years ago
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    R means the set of all real numbers.

  2. anonymous
    • 5 years ago
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    i see, thanks. For this question, is it starts with x=2tcos(s), y=2tsin(s),z=t? what are the next steps?

  3. anonymous
    • 5 years ago
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    i see, thanks. For this question, is it starts with x=2tcos(s), y=2tsin(s),z=t? what are the next steps?

  4. anonymous
    • 5 years ago
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    give me a minute

  5. anonymous
    • 5 years ago
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    ok.\[t=z \implies x^2+y^2+z^2=5z^2 \implies x^2+y^2=\]. your aim is to find a relationship between x,y and z, and get rid of all the parameters.. \[x ^{2}+y ^{2}+z ^{2}=4t^2+\cos^2t+4t^2\sin^2t+t^2=4t^2(\cos^2t+\sin^2t)+t^2\] that's\[x^2+y^2+z^2=5t^2\] , but t=z, \[z=t \implies x^2+y^2+z^2=5z^2 \implies x^2+y^2=4z^2\]

  6. anonymous
    • 5 years ago
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    \[x^2+y^2=4z^2 \] is cone ,, so the parametric equations are correspondent to a circular cone

  7. anonymous
    • 5 years ago
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    The selections of answer are as below: a)\[4z^{2}=x ^{2}+y^{2}\] b) \[2x + 2y + z = 5\] c) \[z = 4 y ^{2}\] d) \[x ^{2} + y ^{?} = 4\] e) \[4z ^{2} = x ^{2} + y ^{2}\] Why are u using x ^{2}+y^{2}\] + z2 = \[5z^{2}?\] how we know it is\[5z^{2}?\]

  8. anonymous
    • 5 years ago
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    The selections of answer are as below: a)\[4z^{2}=x ^{2}+y^{2}\] b) \[2x + 2y + z = 5\] c) \[z = 4 y ^{2}\] d) \[x ^{2} + y ^{?} = 4\] e) \[4z ^{2} = x ^{2} + y ^{2}\] Why are u using x ^{2}+y^{2}\] + z2 = \[5z^{2}?\] how we know it is\[5z^{2}?\]

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