7. The polar equation of the curve r2 + y² = 2x is A T= 2 cos 0 T= sin 20 T= 2 sin 0 B D T= cos e

Q: 6. Consider the polar curve r = 1 – 2 cos(0). Find (a cartesian equation for) the tangent and - the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the slope of the line tangent to the polar curve at the given point. 9 11. r= 9 sin 0; 2' 6 dy…

A: The given polar curve,r=9 sin θ; -92,11π6

Q: 1. Find the equation of the tangent line (s) to the following set of parametric equations at the…

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Q: Consider the following parametric equation. x = 5(cos 0 + 0 sin 0) y = 5(sin 0 – 0 cos 0) What is…

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Q: After finding all the required values, for the polar curve r (0) : sin(0) we can find dy 2 -7 when 0…

A: FOR THE GIVEN INFORMATION

Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²

A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

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Q: 5. Eliminate the parameter to find the equation of the ellips Sx(t) = 4 cos(t) + 1 ly(t) = 3 sin(t)…

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Q: 7. The polar equation of the curve r + y² = 2x is r= 2 cos 0 T= sin 20 T= 2 sin 0 D T= cOs

A:

Q: (b) Given that cos (t) Vos(21) sin' (t) Jos(2)" |cos(2t) dy Find for the parametric equation given…

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Q: 15) (10.) Sketch the parametric curve x = 2 + 3sin(t), y = -3+ 3cos(t) for <t<. Find the slope of…

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Q: dy = cos 20. de dx Given that r= cos 0 ; = - sin 20 and de The slope of the tangent line to the…

A: Given that: r=cosθdxdθ=-sin2θdydθ=cos2θ

Q: (). 3 Calculate the length of the polar curve r = 8 sin' 3 in the interval 0 < 0<.

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Q: Find the exact length of the polar curve. 4 sin(0), o 0S T/3

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Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

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Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0sts2M. 3.1. Find an equation…

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Q: 9. Sketch the polar curve. r = 2 cos 2 0

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Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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Q: The equation of the polar curve above is E. r = 3 + 2 sin 0 F. r = 3 - 2 sin 0 G. r = 3+ 2 cos 0 H.…

A: From the direction of the cardioid, extending horizontally, that you…

Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0S <2M. 3.1. Find an equation…

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Q: 9. Sketch the polar curve.r= 2 cos 2 0 ||

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Q: 4. Find the exact length of the polar 2 cos os 0, 0 < 0 < T. curve r

A: Given: r=2cosθ on 0,π L=Length of Polar curve= ∫ab(r(θ))2+(r'(θ))2dθ now, r'(θ)=ddθ(2cosθ)=-2sinθ…

Q: Which of the following is the equation of the tangent line to the polar curve r = sec at the point 6…

A: Given,r=sec θ2At θ=π3,r = 23

Q: Find the exact length of the polar curve

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Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

Q: Find the exact length of the polar curve described by: r = 5e-0 1 on the interval T <o< 9n. 10

A:

Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 3 cos(0) + 8 sin²(0)) and compute…

A: The objective is to find y(x) and it's it's derivative .

Q: dy dx Given that r= cos 0 ; do - sin 20 and cos 20. de = - The slope of the tangent line to the…

A: Explanation of the answer is as follows

Q: dx Given that r cos 0; dy - sin 20 and do = cos 20. de The slope of the tangent line to the polar…

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

Q: 3. Which of the following is the equation of the tangent () line to the polar curver = sec at the…

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Q: dx dy = Cos 20. do Given that r= cos 0 ; = - sin 20 and d0 The slope of the tangent line to the…

A: Slopes of tangent is dy/dx . Finding dy/dx at theta = 0.

Q: 8 sin ( *(4) in the interval 0 < 0< . Calculate the length of the polar curve r =

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Q: 44. The furthest point from the pole to the polar curve r = 2+ V2 sin 0 occurs when 0 = A. в о C 2

A: Answer

Q: 1 Sketch the curve r=-+sin0 cos 0 ,0 < 0<2n in the polar plane.

A: Any point on the Cartesian coordinate system is represented as x, y. Any point on the polar…

Q: 6. Find the length of the polar curve r = 1+ cos 0 on the interval 0 < 0 < n.

A: Given:

Q: Consider the following parametric equation. x = 3(cos 0+ 0 sin Ø) y = 3(sin 0 -0 cos 0) What is the…

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Q: dx Given that r cos 0; dy - sin 20 and d0 d0 cos 20. The slope of the tangent line to the polar…

A: We will solve the following.

Q: Q1 Find the points of intersection of the polar curves rcos and 2-cos 0-r=0

A: The value of the cosine function  cos0=1cosπ6=32cosπ4=12cosπ3=12cosπ2=0cosπ=-1cos3π=-1cos2π=1

Q: 2. Given the parametric equations x= 2t+ sin 2t and y=1-cos 21, where t is a parameter, dx 2)

A:

Q: 7. [10pts] Calculate the slope of the tangent line to the polar curve r = when 0 cos (0/3) at the…

A: given curve is                                  r=cosθ3 at   θ=π…

Q: 4. Consider the circular helix given by 7(t) = (3 cos t, 3 sin t,4t). Give an equation for the…

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Q: 4. Consider the polar function r(0) = 2+2 cos(20), for 0 E [0, 27). (a) Write parametric equations…

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Q: 8. Find the equation (in terms of Cartesian variables r and y) of the tangent line to the polar…

A: Given curve is Firstly, we find slope of tangent to polar curve is

Q: dx = - sin 20 and de dy = cos 20. de Given that r= cos 0 ; The slope of the tangent line to the…

A: Use the formula for the slope of a polar curve.

Q: 1-For spherical polar coordinate system Zr Zr (2² exp(- 2a 1 Z. -) sin OCosø 42 `a а Jy„V„dV = 8_ =?…

A: For spherical polar co-ordinate system ψpx=142Za32exp-Zr2aZrasinθcosϕTo find:∫ψpxψpxdV=δxx

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

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Q: a. Find the solution set for log, 2+2.log3 x= log, (7x-3) b. Plot the polar curve r 2(1-cose) in…

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.