Question

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?

Answer 1

R means the set of all real numbers.

Answer 2

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

Answer 3

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

Answer 4

give me a minute

Answer 5

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,
\[z=t \implies x^2+y^2+z^2=5z^2 \implies x^2+y^2=4z^2\]

Answer 6

\[x^2+y^2=4z^2 \] is cone ,,
so the parametric equations are correspondent to a circular cone

Answer 7

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\[5z^{2}?\]

Answer 8

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\[5z^{2}?\]