Use De moivres theorem to determine (3-4))"C4cis 30° )ieave your answer in 10 CiS the Formof Fciso

Q: Sketch the set of points (described in spherical coordinates). ρ = 4

A: Sketch the set of points (described in spherical coordinates). ρ = 4

Q: 50. A circle of radius 2 and center (0, 0) can be parametrized by the equations x = 2 cos t and y =…

A:

Q: 7. 2 SECANTS WHOLE WHOLE = WIOLE • OUT SIDE SECANT AND 6. TANGENT IMIDE PIECE • PIECE = PIECE •…

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Q: Describe how the surface with spherical equation p²(1 + A cos² ¢) = 1 depends on the constant A.

A: Given : ρ2(1+Acos2ϕ)=1To describe: How the surface with spherical equation  ρ2(1+Acos2ϕ)=1depends on…

Q: Sketch the segment r = sec 0 for 0 < 0 < . Then compute its length in two ways: as an integral in…

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Q: Find Laplace 2 2 [sin(34) + 65inh czt) ]

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Q: 6. Find the Cartesian coordinates of the point (5, 5, 7) which is in spherical coordinates with the…

A: Topic :- Geometry

Q: A circular helix in xyz-space has the following parametric equations, where θ ∈ R. x(θ) = 4 cos θ…

A: Arc length in 3d We want to determine the  arc length of a  curve given by parametric equation ,…

Q: Convert the point (x, y, z) = (5, 3, - 1) to spherical coordinates. Give answers as positive values,…

A: For converting Cartesian to spherical coordinates use the following expression, p=x2+y2+z2 θ=tan-1yx…

Q: A point has cylindrical coordinates (r, 0, z) = (2, ,2/3). co .Convert to spherical coordinates.…

A: Given cylindrical coordinate is r,θ,z=2,π6,23 ∴ r=2  θ=π6z=23

Q: Chapter 12, Section 12.5, Question 013 Find the curvature and the radius of curvature at the stated…

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Q: Chapter 12, Section 12.5, Question 013 Find the curvature and the radius of curvature at the stated…

A: The given vector-valued function is rt=6cost i+6sint j+7t k at t=π2 to find the curvature and the…

Q: 27 Convert the poínt (58,I,s) from cylincdirical to Spherical Coordinats.

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Q: Show that the cylindrical equationr 2(1 − 2 sin2 θ ) + z 2= 1is a hyperboloid of one sheet.

A: The cylindrical co-ordinates is converted into rectangular co-ordinate as x=rcosθ         ⋯⋯1y=rsinθ…

Q: Transform (4, 7/3, ) from spherical into cylindrical form (here o is any angle).

A:

Q: Discuss the sing ularities Poles fcz) Ze sin z (スー2)(ス-1(+5z+6)Lス+マ)(ズ+り)

A: Singularities are the points at which the numerator of the function is not defined or denominator of…

Q: 7) What will be the coordinates of K' after a +90 degree rotation about the origin? Use parentheses.…

A:

Q: The Cartesian coordinates of a point R are (0, 0, 3). How can this point R be expressed in spherical…

A: Find your answer below

Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

Q: Find all Six trigonometric function values for the angle theta. Sec theta= -square root 5 and theta…

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Q: Show that the cylindrical equation ,2(1 – 2 sin² 0) + z² = 1 is a hyperboloid of one sheet.

A: Given a cylindrical equation r21-2sin2θ+z2=1 To show that this equation is a hyperboloid of one…

Q: Consider a unit sphere centred at the origin. Find an arc length parametrised geodesic connecting…

A: The objective is to compute the arc length parametrised geodesic connecting the points 0,0,1 and…

Q: i) Find the solution of Vu O in spherical co-ordinates.

A: The given Laplace's equation is,∇2u=0Now this equation can  be written as in the spherical…

Q: Sketch the set (described in cylindrical coordinates). θ = π/3

A: Given: θ=π3

Q: Convert the point (x,y,z)=(3,−1,−3) to spherical coordinates. Give answers as positive values,…

A:

Q: Determine the area of the right half of the cardioid formed by r = 7+6 sin 0 14 12 10 8 6 2 -2 -4…

A: Explained below

Q: Find the principle solution of sec(4z) = 2. If there is a distinct solution from the other half of…

A: sinπ3 = 32 and  sinπ-π3=32 cosπ3=12   and   cos2π-π3 = 12 .

Q: 9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere…

A: Given :  The equation ρ = 2 a sin ϕ  cosθ  .   To determine: The equation ρ = 2 a sin ϕ  cosθ  in…

Q: 4. Find the magnetic field at: a. Center solenoid with long 20 cm, 1.4 cm radius and 600 turns…

A: Here, we use the magnetic field formula due to solenoid to get the solution.

Q: y= COsax tor Osxs T Question,

A: The derivative is calculated using first principle

Q: The knuckleball is one of the most exotic pitches in baseball. Batters describe the ball as…

A: The left/right position of the ball when thrown is given by the following function:…

Q: b) r= 3cos(0)-3 sin (0)

A: Idea: substitute x=rCos(theta) and y=rSin(theta) and simplify we get equation in Cartesian form

Q: Convert the point (x,y,z)=(−3,−3,5) to spherical coordinates. Give answers as positive values,…

A:

Q: Transform to spherical coordinates: F 102-8ỹ+6ż at point P (10, 8, 6)

A:

Q: 3. Infer some rosults from the axioms and illustrations of the three- line and four- line…

A: As per your requirement, answer of 3rd part is mentioned below

Q: a: A foree given by ř =gî+2-42 is applied at he pont (l,-t,2). Find 1he moment of Ē about The pont…

A: Concept Used: The Moment (or torque) of the force F⇀ about a point O is calculated by  MO=r×F where…

Q: Convert the point (x, y, z) = ( – 5, 1, – 1) to | - spherical coordinates. Give answers as positive…

A: To convert the given cartesian coordinates (x,y,z)=(-5,1,-1) into spherical coordinates (rho, theta,…

Q: Convert the point (x, y, z) = (- 5, – 2, 4) to spherical coordinates. Give answers as positive…

A: We have to find the spherical coordinate

Q: Is it possible to draw a square in spherical geometry?  Please explain your answer.  How does your…

A: Square in spherical geometry is possible?

Q: yepriate trigonomic subititution to rewrite the intya) U se in the form E sec'e de

A:

Q: If Z, = (-V3 + 3i), Z2 = (2+ 2i ) than 4 in polar form is : %3D Z2 Z1 5n 5n (cos +i sin 12 5n (cos…

A: z1=-3+3i,z2=2+2i,z1z2=-3+3i2+2iApply complex arithmetic rule:  a+bic+di = c-dia+bic-dic+di =…

Q: The circle centered at (4, -3) with radius 11 can be parametrized in many ways, this still happens…

A: center 4,-3radius=11

Q: 9. What will be the coordinates of point Nafter a 270 counterclockwise rotation about the origin?

A: When rotating a point 270° counterclockwise about the origin our point N(x,y) becomes N'(y,-x). This…

Q: Question 4 of 10 To describe a solid in geometry, it suffices to have two dimensions. O A. True OB.…

A:

Q: Čonvert the point (x, y, z) = (1, – 5, 3) to - spherical coordinates. Give answers as positive…

A:

Q: Convert the point (x, y, z) = (-4, 1, 2) to spherical coordinates. Give answers as positive values…

A: Given ' (x, y, z) =(-4,1,2).

Q: The circle centered at (4, -3) with radius 11 can be parametrized in many ways, this still happens…

A:

Q: Convert the point from cylindrical coordinates to spherical co (3,2,0) (p, 0, 4) = || X

A:

Q: Integrate counterclockwise dz by Cauchy's formula 9. - 3 counterclockwise around the circle C : |z –…

A: Given that integrate counterclockwise  ∮Cz2z2-9dz by Cauchy's formula where  C : |z-3-3i|=32π.…

Q: Theorem: Two geodesics at right angles have their torsion equal in magnitude but opposite in sign.

A: To prove: Two geodesics at right angles have their torsion equal in magnitude but opposite in sign.…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.