10. Consider the curve C = {y-x2 = 1} and the vector field F(x, y) = (}, -7). Which points along the curve C is the vector field F tangent to C? A. The vector field is never tangent to C B. Every point of the form (0, y). C. Only the points (0, 1), (V3, -2) , (Vi,-2) D. Only the point (0, 1) E. Only the point (-2, 5)9. Consider the top half (y 2 0) of the region between two circles of radii a and a + 1. Assuming this region has density p(r, y) = veep: what value of a allows the centroid to be at location (I, y) = (0, _)? A. 0 B. 2 C. 5 D. T E. 2xDate _ Page Answer 10 vector field to the curve = yrazz1 is given by F ( my ) = ( 4 , - 2 Now we have. to find vector field on - comp. and y- comp by differ. curve wit. tin and win. to f respectively . M dy dy = an (n . com ponent ) ( y component) dy da -o Nove, Vector field F(ary ) i8 parallel to vector - 2d co L = KX- 2x -0 Now = KXO - 2 - 2 realme Shot on realme 91 5G 2023 07 19 12:32of lacks. ChatGET May 24 Version . . ..". . . . . . ..'.. 20 y = 2 2 + 1 ) Date NOW given curve is The parabola COOT O dev L ( OD ) 21 There is tangent at (or1) which can't be of the form ( yes The & Don't forg because according the given vector activate Of To begin, of radi In Office ap field tangent would be at (0 0) bar point which can be fungent to curve. Hence, The vector field is never None tangent to c . in a pos realme Shot on realme 9i 5G 2023 07 19 12:32Parabol a Answer (a ) coordinates of centroid give density p ( may ) = 1 21 = which A J The suegion between two uncle with vector radii a and atl in top fell two bounded by egos it to never Now find limit of integration by find intersection of two circles ? Q 2= cati) 2 a is negative wwhich is not pading well of possible because be the realme Shot on realme 9i 5G 2023 07 19 12:32Data realme Shot on realme 9i 5G Page Hence, there is no value a that allow centroid to be at location ( ny ) = 0 , 5 ) with given density and region b/w two circle. 2023 07 19 12:36