39 A curve with polar equation r = 3 sin 0 + 25 cos 0 represents a line. This line has a Cartesian equation of the form y = mx + b,where m and bare constants. Give the formula for y in terms of r. For example, if the line had equation y = 2x + 3 then the answer would be 2 - x + 3. y =

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: 2. The curve with polar equation 24 3 cos 0 + 4 sin 0 = is a line. Find the slope and the…

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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…

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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: 2. Graph the given parametric equations using values of t between 0 and 180 degrees. x = 2 cos(3t) ,…

A: Put the values of t in to given equation one by one, find the points

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

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

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Q: Find the slope of the line tangent to the polar curve at the given points. 7-49 cos26. (0.7). (0.-)…

A: Slope of the tangent line at given point for curve r2=49cos2θ

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

A: Let The slope of the tangent line is given as,  Differentiate r with respect to

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: 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: 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: 37. The Cartesian equation of the polar curve 2 = 2a' sin 20 is A. 1? + y? = 4a²xy B. (z* + 3° )° =…

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Q: Find the exact length of the polar curve r=e2(theta) , where 0 is less than or equal too theta is…

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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: 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…

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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…

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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: Find the equation of the tangent line to the polar curve r = 2 – sin(θ) at θ = π/3. Draw

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Q: Find the length of the curve over the given interval.                                     Polar…

A: Given: rθ=5cosθ; θ∈π2,π we know that arc lengthL for any given functionfx over interval a,b is given…

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

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Q: 4. Find a polar equation for the curve represented by the Cartesian equation y = 3x. T = r cos 0, y…

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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: 44 A curve with polar equation r = 7 sin 0 + 36 cos 0 represents a line. This line has a Cartesian…

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Q: 8. First graph the polar curve r= sin(20) on 0<60<2n and plot the point on the curve that…

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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: 6 (1). Consider the curve C of equation (x²-2y+y²)² = x²+y². Among the options listed, select the…

A: We know that a polar coordinate is represented by r, θ, where r is the length with r=x2+y2 and θ is…

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

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

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

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Q: 20 4. An ant walks on a flat surface along a curve with polar equation r= from a point where 0=0 to…

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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: 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: The graph of the polar equation r(0) = 0 cos(0), o ses. with derivative = cos(e) – 0 sin(0), is…

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

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.