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Ainat [17]
3 years ago
8

Consider the vector function given below.

Mathematics
1 answer:
horrorfan [7]3 years ago
4 0
The tangent vector is by definition the derivative of r(t) with respect to t: 

<span>T' = dr/dt = <6t, tsin(t), tcos(t)> </span>

<span>The unit vector T = T'/|T'| = <6t, tsin(t), tcos(t)>/sqrt(36t^2 + t^tsin(t)^2 +t^2cos(t^2)) </span>

<span>T = <6t, tsin(t), tcos(t)>/(t*sqrt(37)) = <6, sin(t), cos(t)>/sqrt(37) </span>

<span>Now the normal unit vector N is perpendicular to r/|r| and T. It is the second derivative of r/|r| with repsect to time </span>

<span>N' = d^2r/dt^2 = <6, sin(t) + tcos(t), cos(t) - tsin(t)> </span>


<span>N= N'/|N'| = <6, sin(t) + tcos(t), cos(t) - tsin(t)>/sqrt(36 + sin^2t +2tsin(t)cos(t)+t^2cos^2t + cos^2(t) -2tcos(t) sin(t) +t^2sin^2t) </span>

<span>N = <6, sin(t) + tcos(t), cos(t) - tsin(t)>/sqrt(37 +t^2)</span>
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Step-by-step explanation:

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Jlenok [28]

Answer:

From the attached diagram, it is clear that:

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It is clear from the blue line graph, that when we add 4 units to the output of the parent function, it will be shifted 4 units up.

Step-by-step explanation:

Given the function

  • f(x) = x³

The graph of the function f(x) is attached below.

We know that when we add the number, let say h, to the function output, it means the graph is shifted 'h' units up.

So, when we add 4 units to the graph f(x), it means the graph will be shifted 4 units up.

Therefore, the graph g(x) = f(x)+4 will be result of shifting 4 units up.

The diagram graph of both f(x) and g(x) is attached below.

From the attached diagram, it is clear that:

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It is clear from the blue line graph, that when we add 4 units to the output of the parent function, it will be shifted 4 units up.

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3 years ago
An someone help m with question 11?
rodikova [14]

Hello,

The square root of each area must be calculated to find the side of the square.

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Bye :)

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