44 A curve with polar equation r = 7 sin 0 + 36 cos 0 represents a line. This line has a Cartesian equation of the mx + b ,where m and b are constants. Give the form y formula for y in terms of x. For example, if the line had equation y 2x + 3 then the answer would be 2 · x + 3. y =

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

A: Given  equation r=2+3sinθwe have…

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: The transform curve of polar equation r 4 cos@+4 sin e to rectangular coordinates (x-2)° – y² = 8…

A: Given that: r=4cosθ+4sinθ

Q: 1. The parametric equations: x = a cos 0,y = a sin? 0;0 ses 2n, define a curve called an asteroid

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Q: ht) A curve with polar equation 9 r = 7 sin 0 + 36 cos 0 ents a line. This line has a Cartesian…

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Q: 19 A curve with polar equation r = 8 sin 0+17 cos 0 represents a line. This line has a Cartesian…

A:

Q: 1. Let C be the polar curve given by r = 2+ sin 0, –T/4<0 <#/2. Sketch the curve. b. Indicate with…

A: Given : C: polar curve=r=2+sin θ,      -π4≤ θ≤π2 (a)   The  graph of the polar curve and  (b)…

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

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Q: a) A curve has the parametric equation given as x = 4+3 cos 0 y = 3 sin 0 – 2. i) Convert the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Show that cos 120 cos 40 – 3 cos 40 sin? 40 and use this identity to find an equation in rectangular…

A: We have to show that cos12θ=cos34θ−3cos4θsin24θ Consider  cos12θ=cos34θ=cos3P        Let P=4θ We…

Q: 39 A curve with polar equation r = 3 sin 0 + 25 cos 0 represents a line. This line has a Cartesian…

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Q: Find the slope of the line tangent to the polar curve at the given point. 11n r= 4 sin e; - 2,-

A: Given,            r=4sinθ ; -2,11π6

Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…

A:

Q: 3. Consider the curve C of equation 4ry r² + y²" Among the options indicated, select the one that…

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Q: Show that cos(18θ)=cos^3(6θ)−3cos(6θ)sin^2(6θ) and use this identity to find an equation in…

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Q: r cos 0 = -3 2n 5Tt 2 3 Check for symmetry line 0 = = pole polar axis

A: rcosθ=-3 Now when θ=0, rcos0=-3⇒r1=-3⇒r=-3 When θ=π6, rcosπ6=-3⇒r32=-3⇒r=-23 When θ=π3,…

Q: 36 A curve with polar equation r = 29 sin 0 + 7 cos 0 represents a line. Write the equation of the…

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Q: 30 A curve with polar equation = 3 sin 8 + 7 cos e represents à line. This line has a Cartesian…

A: Given, a curve with polar equation…

Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

A:

Q: 1. Describe the graphs of the equation (a) r = cos 20 in cylindrical coordinates. (b) p= sec otan 0…

A: First change cylindrical and spherical coordinates system to Cartesian coordinates system

Q: Convert the polar equation 4r cos θ + r sin θ = 8 into a rectangular equation that expresses y in…

A:

Q: 3. Consider the polar curver = sin (0), for 0 € [0, 27). (a) Find the tangent line to the curve at 0…

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Q: 12 A curve with polar equation r = 4 sin 0 + 33 cos 0 represents a line. This line has a Cartesian…

A:

Q: Find dy/dr and the slopes of the tang ent lines shown on the graph of the polar equation r = 2+3 sin…

A: According to question, r = 2 + 3 sin θ

Q: 50 A curve with polar equation r 5 sin 0 + 21 cos e represents a line. This line has a Cartesian…

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Q: Find the length of the curve over the given interval. Polar Equation Interval r= 2a cos e 4 4

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Q: Find the length of the curve over the given interval:    Polar equation: r=5 Interval: [0,pi/6]

A: Given curve

Q: A curve with polar equation r = 8 sin 0 + 49 cos 0 represents a line. This line has a Cartesian…

A: The polar equation is, r=58sinθ+49cosθ   Rewrite the equation. 8rsinθ+49rcosθ=5   Substitute y for…

Q: 12 Find a Cartesian equation for the polar curver = Solve for y and type the simplified solution in…

A: The given equation is: r=12sin θ-15 cos θ...(1) To convert the polar equation to the cartesian…

Q: 7) Find the points at which the polar curve r = 1+ cos® have horizontal or vertical tangent lines.

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Q: 1) The cartesian form of the polar equation (r² cos0 sin® = 4) is? b) (xy)² = 4 a) xy = 4 c) xy? = 4…

A: Since you have asked multiple question,As per our policy, we will solve the first question for you.…

Q: Consider the polar curve with equation r=1+2cos(θ):   (I) The slope of the tangent line to the curve…

A:

Q: 33 A curve with polar equation r 9 sin 0 + 55 cos 0 mx + b,where m and b are represents a line. This…

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Q: A curve with polar equation r = 20 4 sin 0+ 17 cos 0 represents a line. This line has a Cartesian…

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Q: 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

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Q: Find the length L of the polar curve r = 6 sin for 0 < 0 <- 2 2 OL= 12 OL= 6 OL = 6/2 OL = 12 – 6/2

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Q: 10. Consider the curve with polar equation r = 6 sin 0 where 0< 0 <T. WVithout finding the Cartesian…

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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: 23 A curve with polar equation r = 4 sin 0+ 13 cos 0 represents a line. This line has a Cartesian…

A:

Q: A curve with polar equation 16 6 sin 0 + 13 cos 0 represents a line. This line has a Cartesian…

A:

Q: 31 A curve with polar equation r = 3 sin 0 + 7 cos 0 represents a line. This line has a Cartesian…

A:

Q: A curve with polar equation 29 8 sin 0 + 65 cos 0 represents a line. This line has a Carteslan…

A: Given:- r =29/(8sinθ+65cosθ) To find:- Equation of line in Cartesian form

Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

A: see below the answer

Q: 7 A curve with polar equationr = 5 sin 0 + 31 cos 0 represents a line. This line has a Cartesian…

A: topic - change in coordinate system

Q: 15) Find the slope of the tangent line to the given polar curve at the point specified by the value…

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Q: A ball is thrown at an initial height of 50 feet at an initial velocity of 65 feet/second at an…

A:

Q: A curve with polar equation 32 3 sin 8 + 13 cos e represents a line. This line has a Cartesian…

A:

Q: 23 A curve with polar equation r : 4 sin 0 + 13 cos 0 represents a line. This line has a Cartesian…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.