Let r(t ) = ti + cost j + t? k be a space curve. Which of the following vectors is parallel to the tangent vector of the curve at (0,1,0)? O a. < 0, 2, 0 > O b. < 1, 0, 2 > O . < 2, 4, 6 > Od.< 4, 0, 0 > Oe.<1, 0, 1 >

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A: The given curve is: r(t)=t3,t2,1tr'(t)=3t2,2t2,-1t2 Now, the given point is r(1). So, r'(1)=3,2,-1…

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Q: Let r (t ) = ti + costj + t? k be a space curve. Which of the following vectors is parallel to the…

A: Solution:

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A: GIVEN: r(t) = {3t, t2 + 6t, t3}

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A: See the attachment.

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A: I have appended the formula used in the solution part of the question

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A: Radius of curvature of teh function is given by formula, R = (1+y'(x)2)32y''(x)

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A: According to question given thatr(t)=t3 i + t2 j + 1t k

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A: we have,r(t)=cost2i+sint2jhere,x=cost2andy=sint2we know…

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A: The given expression of the curve is, Differentiate the above expression with respect to t.

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A: We use the following formula to find the unit tangent vector T(t)=V(t)/|V(t)|

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Q: ; Consider the vector function r(t) = ti + t²j+t°k. Compute the curvature of r at time t = 2.

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.