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PIT_PIT [208]
3 years ago
11

How do you find the parameterization of a helix?

Mathematics
1 answer:
Marina CMI [18]3 years ago
7 0

Answer:

\left\{\begin{array}{l}x=r\cos t\\ \\ y=r\sin t\\ \\z=at\end{array}\right.

Step-by-step explanation:

A <u>helix</u> is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not directly above the other) is a fractional turn of a helix, as can be seen by cutting the cylinder along one of its sides, flattening it out, and noting that a straight line connecting the points becomes helical upon re-wrapping (see attached diagram for helix).

The parametrization for the helix is

\left\{\begin{array}{l}x=r\cos t\\ \\ y=r\sin t\\ \\z=at\end{array}\right.,

where r is the radius of the helix, a is the constant, and t\in [0,2\pi ) is the parameter

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On mobile devices, global voice traffic has been growing by approximately 222 petabytes (\text{PB})(PB)left parenthesis, P, B, r
loris [4]

Answer:

Voice data consumed: 118PB

Global data consumed: 144PB

Step-by-step explanation:

At a given month voice and data trafic are equal at 110 PB each

Rewriting the info into formulae will give us

Voice_Data=Prev_VD+2PB*Month

[tex]\left \{ {{Global\_Data_{(M+1)}=Global\_Data_{(M)}*\left(1+0.07\right)} \atop Global\_Data_{(M+2)}=Global\_Data_{(M+1)}\left(1+0.07\rigt)=Global\_Data_{(M)}\left(1+0.07\right)^2} \right. \\  \\

It follows: Global\_Data_{(M+N)}=Global\_Data_{(M)}}\left(1+0.07\right)^N[\tex]

where we rewrite the percentage as a ratio (dividing by 100)

One grows at a constant rate,and the other grows at a rate that depends on the Data already consumed.

Knowing that at one point they are the same, we can use that value as Previous voice data and previous global data:

Voice_Data=110PB+2PB*Month

Global_Data=110PB*(1+0.07)**Month

To see what happens after 4 months, simply replace the Month value by 4 and evaluate:

3 0
2 years ago
What is the coefficient in the following expression?
frosja888 [35]

Answer:

5

Step-by-step explanation:

A coefficient is a number used to multiply a variable. in "5a" 5 is the coefficient.

4 0
3 years ago
Solve 3x^2=-12-6x by completing the square​
Lelu [443]

Answer:

x = - 1 ± i \sqrt{3}

Step-by-step explanation:

Given

3x² = - 12 - 6x ( add 6x to both sides )

3x² + 6x = - 12 ( divide through by 3 )

x² + 2x = - 4

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(1)x + 1 = - 4 + 1

(x + 1)² = - 3 ( take the square root of both sides )

x + 1 = ± \sqrt{-3} = ± i \sqrt{3} ( subtract 1 from both sides )

x = - 1 ± i \sqrt{3}

3 0
3 years ago
Increase £14187.13 by 14.5%
zhenek [66]

Answer:

16,244.26

Step-by-step explanation:

14,187.13 + (14.5% × 14,187.13) =

14,187.13 + 14.5% × 14,187.13 =

(1 + 14.5%) × 14,187.13 =

(100% + 14.5%) × 14,187.13 =

114.5% × 14,187.13 =

114.5 ÷ 100 × 14,187.13 =

114.5 × 14,187.13 ÷ 100 =

1,624,426.385 ÷ 100 =

16,244.26385 ≈

5 0
3 years ago
Read 2 more answers
Write 51% as a fraction in simplest form
olga_2 [115]
51/100 is the answer


3 0
3 years ago
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