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Marrrta [24]
3 years ago
5

Identify the surface with the given vector equation. r(s, t) = s sin 4t, s2, s cos 4t

Mathematics
1 answer:
k0ka [10]3 years ago
4 0

Answer:

Circular paraboloid

Step-by-step explanation:

Given ,

r(s,t)=ssin4t,s^2,scos4t

Here, these are the respective x,y,z axes components.

  • <em>Component along x axis r_i : ssin4t</em>
  • <em>Component along y axis r_j : s^2</em>
  • <em>Component along z axis r_k : scos4t</em>

We see that , from the parameterised equation , r_i^2+r_k^2=s^2sin^24t+s^2cos^24t\\r_i^2+r_k^2=s^2\\r_i^2+r_k^2=r_j

This can also be written as :

x^2+z^2=y

This is similar to an equation of a parabola in 1 Dimension.

By fixing the value of z=0,

<u><em>We get y=x^2 which is equation of a parabola curving towards the positive infinity of y-axis and in the x-y plane.</em></u>

By fixing the value of x=0,

<u><em>We get y=z^2 which is equation of a parabola curving towards positive infinity of y-axis and in the y-z plane. </em></u>

Thus by fixing the values of x and z alternatively ,  we get a <u>CIRCULAR PARABOLOID. </u>

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When will n(A∩B)=0? Explain and give an example.
andrew11 [14]

Answer:

Two sets are called disjoint if they have no elements in common. For example:

The sets S = { 2, 4, 6, 8 } and T = { 1, 3, 5, 7 } are disjoint.

Another way to define disjoint sets is to say that their intersection is the empty set,

Two sets A and B are disjoint if A ∩ B = 0.

In the example above,

S ∩ T = ∅ because no number lies in both sets.

Step-by-step explanation:

8 0
3 years ago
5y+4 times 2 what is the coefficient in this expression?
rodikova [14]

Answer: 5

Step-by-step explanation: The coefficient is the number that comes right before the variable. Another way to say this is it's what the variable is multiplied by.

3 0
3 years ago
If x=-5 what is the value of x^2-1/x+1? A. 6 b. -4 c. 4 d. 5 4/5 e. 19 <br> need answers asap
xxTIMURxx [149]

Answer:

The answer is -6 but its not in the option

Step-by-step explanation:

\frac{ {x}^{2} - 1 }{ x  + 1}

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[(-5)²-1]/(-5+1)

= (25-1)/(-4)

= 24/-4

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4 0
3 years ago
Whats the gcf of 32 and 52
Molodets [167]
The greatest common factor of 32 and 52 is: 4

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Factors of 52: 1, 2, 4, 13, 26

The common factors between them are 1, 2, 4, but the greatest common factor between them is 4.


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