Lse shokes' thevrem to evolubte ∬s ourt F. cs.F(x,v,⩾)=v2(t+xcos(t)j+xzsin(y)k, Sis the hemisphere x2+y2+z2=4,y≥0, oriented in the direction of the positive y-axis Get tutor helpUse Stokes' theorem to evaluate ∬S curl F⋅dS.F(x,y,z)=zeyi+xcos(y)j+xzsin(y)k,S is the hemisphere x2+y2+z2=4,y≥0, orlented in the direction of the positive y-axis Get tutor helpsin30tan230∘(5)cos30∘=cot45∘Question 22. In the liqute (3;5),B(x:5),((5,3) and D(1;1) are the vertices of paralletogetam ABC (5) AC and BD) the diagonals of the parallelogram, intersect at E.2.1Determine :2.11The coordinates of :-21.2The condinates of B2.13The coordinates of the midpoint F, of CD and hence the gradient of theL line Perpendicular to CD. Get tutor help8A) REGULARITY Determine whether △DEF≅△PQR.D(−6,1),E(1,2),F(−1,−4),P(0,5),Q(7,6),R(5,0)Find the side lengths of each triangle.DE=52,PQ=52,EF=10,QR=10,DF=52,PR=52DE=2,PQ=2,EF=10,QR=10,DF=2,PR=2DE=52,PQ=52,EF=210,QR=210,DF=52,PR=52DE=52,PQ=510,EF=210,QR=210,DF=510,PR=528B) Fill in the blanks using the available answer choices.Is DEF≅△PQR ? Explain.△DEF to DE=52,PQ=52,EF=10,QR=10,DF=52,PR=521 by DE=52,PQ=52,EF=10,QR=10,DF=52,PR=522 because corresponding sides have and are (Blank I)(Blank 2)(Blank: 3)Blank 1 optionsBlank 2 optionsBlank 3 options- is congruent- the same measure- is not congruent- different measures- congruent- not congruent Get tutor helpEvaluate the integral, where E is enclosed by the parabolold z=9+x2+y2, the cyllinder x2+y2=5, and the xy-plane. Use cylindrical coordinates.∭Ee2dvStep 1In cylindrical coordinates, the parabolold z=9+x2+y2 has the equation z=9+r2,9+r2 and the cylinder x2+y2=5 has the equation r=5Sim2Therefore, the reglon E enclosed by the parabolold, the cylinder, and the xy-plane is described byE={(r,θ,z)∣0≤z≤□□.0≤r≤5,0≤θ≤2π Get tutor help5. The equation of the tangent to the curve y=kx+x6 at the point (−2,−19) is px+qy=c. Find the values of the integers k,p,q and c, where c>0. Get tutor help