Evaluate Re z? dz, C: the unit circle (counterclockwise).

Q: Given: Isosceles trapezoid АВCD Equilateral AFBC Right ΔΑED ВС 3D 12, АВ 3 5, B and ED = 16 Find: а)…

A: As ABCD is an isosceles trapezoid. Therefore, the length of AB and CD will be same. CD=5  Triangle…

Q: If C is the unit circle x² + y? = 1 oriented counterclockwise and F (x, y) = xi +y j, what is the…

A:

Q: 16. Find the length of in the circle. Y is the center point. YZ = 5, and MLXYZ = 45. %3D rloso eme…

A: We have given a circle and the radius of the circle YZ=5 angle XYZ= 450

Q: Given C is the unit circle z =1, then z dz = %3D -2 Ti None

A:

Q: The angle formed between A = 5a, +10ag+ 10az and surface z 5 is 10 15.1 74.97 48.189

A: There are two types of quantities which describe the magnitude and direction of an object and are…

Q: In the circle R, what is mzSRT if arc AST is a semicircle and mzSRA = 74? * A T O 106 O 53 74 Option…

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Q: Given C is the unit circle z=1, then dz = %3D None 2 T - i - 2 Ti

A:

Q: In the diagram below, tangent AB and secant ACD are drawn to circle O from an external point A, AB =…

A: Use property of tangent line and secant line

Q: %3D In circle H with mZGKJ = 27, find the mZGHJ. J

A:

Q: If C is the unit circle x² + y² = 1 oriented counterclockwise and F(x, y) = x F. dR? -T 2π TT î 1 C…

A:

Q: Show that the area of a triangle

A:

Q: х2 — 9х + 14 у — 3 3

A: A quadrilateral has four straight sides .A pairs of opposite side are parallel then the…

Q: In the following sketch, O is the centre of the circle. AD = AC. AC=3 cm and BD=1 cm. B Determine,…

A: Angle subtended by a diameter at circumference of a circle is always 90 degree.

Q: Which of the following three dimensional figures, in the orientation given, can produce a triangle…

A: Since, we get a triangle when cut by a plane. Therefore, the 3-D figure is prism.

Q: Evaluate f, z dz, where C is the unit circle in the counterclocwise direction. O 2ni O 4ri O -2ni

A: Given: ∮C Z¯dz we will use the the result: Given the ingredients we define the complex line…

Q: In the circle below, O is the center, VT is a diameter, PU intersects the circle at T, and SW…

A:

Q: Sa(Va sin r, r3 + 3xy?) dr, where C is the circle x? + y? = 1, oriented clockwise. %3D

A:

Q: Which sequence of rigid motions will definitely work to take triangle GHJ U H. Rotate GHJ using…

A:

Q: t Sci. ENGLISH LANGUA. Q Anthem Review Fla. the diagram below of circle O with diameter BC and…

A:

Q: By Green's theorem, if C is the circle r + y = 4 taken anticlockwise, then z*dy, equals -27. none of…

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Q: Evaluate ry dr +r dy, where C is the positively oriented triangle enclosed by the lines y = I=0 and…

A:

Q: ABCD is a parallelogram DB intersects AE at point F Given: AF АВ Prove: EF DE D E A

A: ABCD is a parallelogram in which DB intersects AE at point F

Q: If C is the circle |2| = 2, given clockwise, then the integral Sc dz is (z–41)² Select one: O a. -2…

A:

Q: Evaluate ry* ds where C is the right half of the circle a? + y? = 4

A: First convert the equation of circle into parametric form.

Q: E Cl. 10 11 12 9. Which of the following is a chord but not a diameter of the attached circle? JK…

A:

Q: In the diagram below, AB and CD are bases of trapezoid ABCD. D A B (Not drawn to scale) If m/B = 123…

A: If m∠B = 123° , & m∠D = 75°m∠C= ?AB|| DC∠A +∠D = 180°& ∠B+∠C = 180°

Q: T. /115° R A,

A: Given figure is isosceles trapezoid.

Q: In the diagram below of AACT, D is the midpoint of AC, O is the midpoint at AT, and G is the…

A:

Q: By Green's theorem, if C is the circle z+y =D4 taken anticlockwise, then 'dy, equals

A:

Q: Show that, C : |z| = 3, |S, z3 – z?-3 c z4– z2+4 dz|s 117 TT 34 5. Evaluate 9. zt; sin 3z dz, where…

A: The given problem is to show the absolute value of the contour integral over given region and…

Q: In the following sketch, O is the centre of the circle. AE= ED and DT=TC. %3D Prove that (1) Ê =Ô¡…

A:

Q: If Tis the midpoint of SU, what are ST, TU, and SU? 6x 3x +27

A:

Q: In the circle centre O, BO OD, 2. AE = EC and AÔD = 116°. %3D Calculate the size of: (a) (b) АВС D B…

A: Given: ∠AOD=116°∠BOD=90°                  ∵ BO⊥OD

Q: The following triangle can best be classified as: O both equilateral and equiangular O equilateral O…

A:

Q: Consider AXYZ (not shown). a) Which side is included by ZX and LY? b) Which angle is included by…

A: Draw the triangle ∆XYZ.

Q: In the diagram below of triangle RST, U is the midpoint of RT and V is the midpoint of ST . If mZT…

A: Triangle Question

Q: 16. In circle Z, if VZ = ZW, SV = 21, and mUT = 112°, find each measure. %3D U a) UT = d) mXT b) WT…

A:

Q: ZXYZ is an inscribed angle in circle O with m XZ= 127°. Determine the m/XYZ. 127° 0. Y 63.5° 53° C…

A: the Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the…

Q: Find the semiperimeter s of triangle ABC. a = 3.1 m, b = 2.5 m, c = 2.7 m s =

A: Known fact: Let a, b and c are sides lengths of triangle. then semi perimeter is given by s=a+b+c2.

Q: (i) Evaluate $.z'dz, where C is the positively oriented circle |z- 1| = 1.

A:

Q: In circle O, m.JM = 130°, and ZT 45°. %3D J N R M. What is the mNR?

A:

Q: The midpoint of AB is M(6, 1). If the coordinates of AA are (4, 8), what are the coordinates of BB?

A: M has coordinates (6,1) Coordinates of A =(4,8)

Q: The image shows a circle with diameters AC and BD. Prove that chords BC and AD (not drawn) are…

A: Find your answer below

Q: What is the radius of the given contour C: |z+5i| = 7+7, 0<0< 2n

A:

Q: the dis fance from Pla.y,z) to the origion o d and fe clis fance from Pto ACo.003) is de .writeian…

A:

Q: 16. Rhombus. A B MZABD = %3D E mZA = 3 DC = 36°

A:

Q: Plot the image of quadrilateral ABCD under a reflection across line . C D

A: Reflection is a transformation representing the flip of the figure. If we are reflecting a figure…

Q: 8. If C'is the circle |z – 1| = In the counter-clockwise direction, what is fa sScdz? z-1 27i 2rie…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.