Evaluate cz dz, where c is |z| = 1 zG-2) Inz %3D

Q: S = {(x, y, z) E R : 2 = x² + y°, 0 s 4}. Evaluate e* dS. ds.

A: To evaluate the surface integral over the surface S is given by the equation z=gx,y, use the…

Q: (a) D = (x + z)a, (b) E = (y² – x³)a, + xyza, + (x² – z?)a.

A:

Q: Find the value af Z そf え e = 1+3 i

A: for log of complex number we know that, x + iy = log(a+ib) then, x + iy = log|r| + i(theta) where,…

Q: Given: z = a' + æy", r = uv² + w®, y = u + ve" az Find when u = 2, v = – 3, w = 0 dv

A:

Q: tind the Value of d that makes the systom has (2) uniqe Sdubion. 3X-2y= (b) No . Solation X+Xy = 2…

A:

Q: 327. F(x, y, z) = zi+ xj+ yk; S is hemisphere z = (a² – x? – y?)/2. -

A:

Q: If f(x, y) = e + e", then Vf(x, y) = (0, e³). Select one: OTrue OFalse

A:

Q: P(e) = (c,). what is the value of csc () + sec 0? 3 27c + 9c + 3c+1 9c (c+3)3 9c (3c+ 1)3 9c c + 3c?…

A: We are asked evaluate the following.

Q: The calculation of the df for the χ2 test of independence is   r × c   r × c − 1   (r − 1)(c − 1)…

A: Option :-  (r-1) (c-1)  Followings are the Explanation of the question  when calculating the…

Q: SL (e,9) f(x, y) = dx dy f(x, y) dy da 0. 0. 0. O True O False

A:

Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and dv S…

A:

Q: Find the value of c such that P(Z > c) = 0.28 %3D O a. 0.3 O b. 0.58 O c. 0.85 O d. 0.22

A:

Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (e) z = exs ; x = s2 + 2st, y = 2st + t2

A: Given:To Find (∂z)/(∂s) and (∂z)/(∂t)(e) z = exs  ; x = s2 + 2st, y = 2st + t2

Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

A:

Q: Let X: EXP(0). suppose Y= 2x , the Y is i = 1 Select one: a. Gamma (n,-) b. Camma(n. 4) С.…

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: For a function y(x), the quantity dydx represents the first derivative of y. This quantity…

Q: Find Duf at P. f(x, y, z) = 4x'y°z?; P(1, – 2, 1); u = - 2. Duf

A: The objective of the question is evaluate the directional derivative at a given point.

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: we know that lnmn=lnm+lnn similarly, ddxlncx=ddxlnc+lnx=ddxlnc+ddxlnx…

Q: (b) Hạ: u < HO,n = 30, t = 2.431 = 0.011 P-value %3D

A: Given : Ha : u &lt; uo  n = 30  t = 2.431

Q: ~(QヘP)=P v~Q =P V ~Q ylgn ihi

A:

Q: %3D AB is a midsegment of AXYZ. If AB = 13, what is the measure of XY? A 13 B

A: Given information: AB is the midsegment of a triangle XYZ. length of AB is 13 units.

Q: Evaluate p xy*dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,3), and (0,3)

A: *Concept:- Use Green's theorem.

Q: if x? + y? = 4 then prove that = d'y dx %3D

A:

Q: Let D, E ⊂ C be starshaped w.r.t the same z∗ ∈ D ∩ E. Show that D ∪ E, D ∩ E are starshaped

A:

Q: Find /| v'e*** - y? when D={(x,y)E R? | x>0,y>0,x² + y?<1}

A:

Q: Ir If z = f(x- y), then of df дх ду 1 -1 12 O 5

A: → Use chain rule of differentiation.             ∂(f(g(x)))∂x=∂(f(g(x)))∂(f(x))×∂(f(x))∂x→While…

Q: S[(vxvø)•nds, The value of where o(x, y, z) is defined on S is (a) 1. (b) 0. (c) 2x.

A: Concept:

Q: Evaluate ff, (x - y + 1)dxdy, where R is the region inside the unit square in which x + y = 0.5. |

A:

Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3).

A: The solution is given by using greens theorem as follows

Q: The expression for Absorption law is given by Select one: a. A + AB = B b. A + AB %3D А с. А + В %3D…

A: Here I am attaching image so that you understand each and every step.

Q: Evaluate II, (z*y +) dz dz dy, where D = [0, 1] × [0, 1] × [1, 2]. %3D

A: Here we have to find the integration if triple integrate: ∭x2y+1zdzdxdywhere D=0,1×0,1×1,2Thus it…

Q: Evaluate o -dz where C :|z| = %3D (z-1) (z² – 5z +6) C

A:

Q: What must be the measure of ZX in order for ARST to be similar to AXYZ? AA 10 40° R 4 А. 20° 32° C.…

A: Here  In ∆RST and ∆ XYZ  As ratio of sides are same  RS/XY = 10/5 = 2 and RT/XZ =8/4 = 2

Q: f(x) = In(x), n = 4, c = 3 Pa(x) = %3D

A:

Q: If z=u²+uv , u=x-2y, v=2x– y , find the value of when x=1 and y=-1. dx а. 13 b. 5 O c. 7 9

A:

Q: Let I:=∬DydA, where D={(x,y): y≤x≤4, 0≤y≤1}.  The value of I is?

A:

Q: S = {(r, y, z) E R³ : 2? = x² + y°, 0 s< 4}. %3D Evaluate e dS.

A:

Q: Evaluate ∭B ze x+y dV where B is the box determined by 0≤x≤5, 0≤y≤1, and 0≤z≤4 The value is

A: the integral given to us is  ∬∫Bzex+ydV                (1) where B is s the box determined by 0≤x≤5,…

Q: E(x, y, z) = xi+ yj + zk

A: Given data:     The given vertices of the cube are: . The given expression for the electric field…

Q: Iff, g e R(x) on [a, b), prove that f? dx + g? dx 2 2 Ifg | dx.

A: Given that, f, g∈Rx on [a, b]We need to prove that∫abf2dx+∫abg2dx≥2∫ab|fg|dx

Q: dx If S V(4+x?)3 = Sh(0) d0, then h(0) de %3D A 1 D 4 (B

A: Given : ∫dx(4 + x2)3 = ∫h(θ) dθ   To find ∫0π2 h(θ) dθ.

Q: e |/ (x² + y³) dV, where E = {(x, y, z) E R³ : VA- x² – y? <z< V9– x² – y?}. Evaluate E

A: The region E will be bounded within the upper half of the spheres x2+y2+z2=(3)2 and x2+y2+z2=(2)2.…

Q: S„Xg (x)dm , where E = { x : x € Q , -1< x<1 } %3D

A:

Q: If // f(x,y) dA > 0. then f(x, y) ≥ 0 for all (x, y) in D. D

A: answer is in next step. please give a like !!

Q: Evaluate x dV E where E = {(x, y, z) E R³ | 0 < z < x+ y,0 <x < y?,0 < y < 1}.

A: Given: Now,                ∫01∫0y2∫0x+yxdzdxdy=∫01∫0y2xx+ydxdy=∫01y52+y63dy=1184

Q: Find the length of DE. Given: DE || GH;EH = x; EF = 2x E 4у — 6 Зу— 18 H. 2x F

A: It is given that, DE∥GH , EH=x ; EF=2x We have to find the length of DE.            Given that,…

Q: ue of a and c are and

A:

Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

A: ANSWER: OPTION 2nd

Q: Evaluate z cosz dz where C is (1)|z – 1| = 1 (i)피 = 2

A: Answer

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.