Suppose \vec{f}(x, y) = -y \sin(x) \vec{i} + \cos(x) \vec{j}.

(a) find a vector parametric equation for the parabola y = x^2 from the origin to the point \left(3,9\right) using t as a parameter.
\vec{r}(t) =

(b) find the line integral of \vec{f} along the parabola y = x^2 from the origin to \left(3,9\right).
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0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl