The curves r1(t) = 2t, t2, t4 and r2(t) = sin t, sin 5t, 2t intersect at the origin. Find their angle of intersection, θ, correct to the nearest degree.

Therefore the angle of intersection is

Step-by-step explanation:

Angle at the intersection point of two carve is the angle of the tangents at that point.

Given,

and

To find the tangent of a carve , we have to differentiate the carve.

The tangent at (0,0,0) is     [ since the intersection point is (0,0,0)]

     [ putting t= 0]

Again,

The tangent at (0,0,0) is    

       [ putting t= 0]

If θ is angle between tangent, then

Therefore the angle of intersection is .

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

1

step-by-step explanation:

it's the only multiple of both and the least