Find a formula f⃗ =⟨ f1(x, y), f2(x, y) ⟩ for the vector field in the plane that has the properties that f⃗ (0,0)=⟨0,0⟩ and that at any other point (a, b)≠(0,0) the vector field f⃗ is tangent to the circle x2+y2=a2+b2 and points in the clockwise direction with magnitude ∥f⃗ (a, b)∥=2a2+b2√.

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

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm