In Problems 7-12, identify the conic that each polar equation represents. Also give the position of the directrix. 1 3 4 7. r = 8. r = 9. r = 1 + cos 0 1 - sin 0 2 - 3 sin 0 2 3 6. 10. r= \1. 12. r = 1 + 2 cos 0 4 - 2 cos 0 8 + 2 sin e

Q: Problem 3. Calculate the first fundamental forms of the following surfaces: (a) x(u, v) = (u - v, u…

A: According to guidelines we should have been able to solve only first question at a time #3

Q: Use the identity cos 20 = cos² 0 – sin² 0 to find a polar equation of the hyperbola x² – y² = 1.

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Q: 3Q: If z₁ = 1.5 cisand z₂ = 4 cis(-7) find and express it in the rectangular form.

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Q: Problem 3: The equation ax + by + cz = 0 describes a plane in R that passes through the origin. The…

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Q: Problem #5 Find dy/dx and d'y/dx², for the following parametric equations. x = 2+t², y=t² +t³ 3

A: We have to find dydx and d2ydx2 for the following parametric equations - x = 2 + t2y = t2 + t3

Q: In Problems 35–38, find parametric equations that define the curve shown

A: Disclaimer: Since you have posted a question with multiple questions, we will solve the first three…

Q: Chapter 5, Problem 5/185 Determine the x- and y-coordinates of the centroid of the shaded area. 30 |…

A: To find: x and y coordinates of centroid of the shaded region . from figure you can see that from…

Q: 47. Show that every line that does not pass through the origin has a polar equation of the form sin…

A: Let's understand the relationship between polar coordinates and Cartesian coordinates. Please see…

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. Given an equation of a conic in polar formr= f(0), substituting (0 – a) results in a…

A: Given an equation of the conic in the polar form r = f(θ), Substituting θ - α results in a…

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: Problem 2. (6 Points) Calculate the first fundamental forms of the following surfaces: (a) x(u, e)…

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Q: Problem 2 You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…

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Q: Problem 3. Calculate the first fundamental forms of the following surfaces: (a) x(u, v) = (u – v, u…

A: Hi! You have posted multiple questions. As per the norm, we will be answering only the first one. If…

Q: Graph the line and conic section. r = 1/(1 + 2 cos u)

A: To graph r  = 11 + 2 cos u.

Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: Problem 5 Let D be the region in the ay-plane where * + y < 2r, * + y* < 1 y 20 and and For any…

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Q: Is the given statement true or false? Justify your answer. Directrix of a conic r = 10 3-2 cos 0 is…

A: Given: r=103-2 cos θis x=13

Q: 10 Convert the Cartesian equation 2 xy = 1 in polar equation form. r²cos2θ = 0 cosθsinθ = 1/2…

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Q: In Problem,match each of the graphs (A) through (H) to one of the following polar equations..θ =3π /…

A: To draw: The graph of θ=3π4. Given information: The angle is θ=3π4. Explanation: Suppose a ray…

Q: Use Problem 6 to show that the area inside the ellipse x = a cos θ, y = b sin θ,0 ≤ θ ≤ 2π, is A =…

A: To show that the area inside the ellipse x=acosθ,y=bsinθ,0≤θ≤2π is A=πab. We know that…

Q: 1 a. Showing all 9r2 = (1 + 3r cos 0)². b. Express 9r2 = (1 + 3r cos 0)² in rectangular coordinates.…

A: a. Consider the equation: r=13-3 cos θ

Q: Is the given statement true or false? Justify your answer. 10 3-2 cos 0 is a = 13. Directrix of a…

A: The given polar equation is r=103-2cosθ. Rewrite it as follows.

Q: In Problem,match each of the graphs (A) through (H) to one of the following polar equations. r = 2

A: Given polar equation r = 2

Q: Graph the line and conic section. r = 8/(4 + cos u)

A: Graph the line and conic section. r = 8/(4 + cos u)

Q: In Problem,identify the conic that each polar equation represents and graph it.

A: We know that the general Cartesian form of a curve is : Ax2+Bxy+Cy2+Dx+Ey+F=0 Determinant=B2-4AC.

Q: In Problems 39–62, identify and graph each polar equation

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Into polar coc x2 + y² = 3x %3D

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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: Problem #4: Evaluate the following integral, xyz dS, where S is the surface with parametric…

A: We will find out the required value.

Q: Problem 29: Transform the parametric equations x= cos 0, y = cos? 0 +8 cos e into its corresponding…

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Q: 12.3: Problem 9 Convert the integral dy dx to polar coordinates and evaluate it (use t for 0):…

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Q: (x- 2), (y-6)² Problem #4: Find the slope of the line tangent to the conic section =1 at 16 25…

A: This question is related to Straight lines, we will solve it using given information.

Q: Problem 8.2. Each part of this problem contains a double integral. In each case, you should first…

A: We have to use relation between cartesian and polar co ordinate  x= r cosθ , y=r sinθ and  dA= r dr…

Q: Problem #4: Find the slope of the line tangent to (х-3) + (y-2)² = 1 at (3,7). the conic section 36…

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Q: Problem 6 / (3y – xª + 2) dx + (5x + sin y*) dy, where C is the counterclockwise- Use Green's…

A: Given ∫C3y-x4+2dx+(5x+siny3)dy Where C is the counterclockwise oriented boundary of the triangle…

Q: Give an example of two polar equations, r1(0) and r2(0), whose graphs intersect in at least two…

A: According to the given information, it is required to give an example of two polar equation whose…

Q: What is (x - 12)² + y² = 144 in polar form? r = 24 sin 0 r= 24 cos 0 O Option 1 r= -24 sin 0-144…

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Q: Question 9. A circular helix in xyz-space has the following parametric equations, where 0 e R. 4 cos…

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Q: Practic Problem # 2.5 RS that Find the parametric equa tious of the liue in through the poiuts.…

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Q: question 1

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Q: QUESTION NO:02 The (a) of Ihe moment of inerla rolation Find disk for The 0 X-ăris ii) Y-asis i)…

A: The objective is to find the moment of inertia of the disc By using the parallel axis theorem…

Q: 9.45.) (a) Use the figure to show that x =r cos ø, y = r sin ø and x' = r cos( ø – 0),y' = r sin (4…

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Q: (x- 2)² , (y-6)² Problem #4: Find the slope of the line tangent to the conic section =1 at 16 25…

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