(iii) 3rd subplot is A butterfly curve using polar coordinates: 2a - I r = esina – cos(4a) - sin( 24 -), where a takes 500 values from O to 8 T.

Q: A curve with polar equation r = 42 6 sin(0) + 31 cos(0) y = has Cartesian equation:

A: cartesian equation is y=7−631x​Explanation:Step 1:given that r=6sinθ+31cosθ42​using cross…

Q: Consider curve C of equation (x2 −2y + y2)2 = x2 + y2. Among the options indicated,select the one…

A: Consider curve C of equation (x2 −2y + y2)2 = x2 + y2. Among the options indicated,select the one…

Q: Consider curve given in polar coordinates by Find the derivative r = 8 cos 0,0 ≤ 0 ≤T/2, dr do -8…

A: The given curve is: r=8cosθ;  0≤θ≤π2. To Do: Find the derivative drdθ. Compute the surfaced area…

Q: Graph the following polar function r = f(0) =V4-3 sin 20 on the interval 0<0<2n , and find %3D the…

A: We have polar function given and we have to graph the function and find the area of this sector.

Q: Consider the polar curves C₁ : r = 2 - cas 0 and C₂: r = 2 + 2 cos 0, 0 € [0, 2πC). (1.) Show that…

A:

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: 5. Consider the polar curve r(0) = -2 cos 0 (a) Circle the polar curve that matches the r(0) above.…

A: The given problem is to sketch the given polar curve r(theta)=-2cos(theta).

Q: How many times do the graphs of the polar curves r=3 and θ=π/6 intersect?

A:

Q: Sketch the curve with polar equation r = cos(3θ), 0 ≤ 0 < 2π, plotting only the points with r≥ 0 and…

A: The given problem is to sketch the given curve with polar equation r=cos(3theta) for 0&lt; theta&lt;…

Q: b) The length in first quadrant of the curve x/3 + y2/3 = a²/3 is given by 6ac/2 where parametric…

A:

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

A:

Q: Sketch the curve with polar equation r = cos(30), 0 ≤ 0 < 2π, plotting only the points with r≥ 0 and…

A:

Q: Q2 Find the points of intersection of the polar curves r=1+cos 9 and r= -cos

A: Point of intersection of the Polar curve

Q: Find a Cartesian equation for the curve represented by the given Polar equation. (a) r = -2 (b) T =…

A: We have polar form equationWe have to convert it in cartesian form

Q: Draw the polar curve to ((x-3)2/32) - (y2/32) = 1

A: We have to draw the polar curves to x-3232-y232=1.

Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

A:

Q: Plot the following curves in polar coordinates. 50 (52) 1. r = 2 + cos

A: We have to graph the given polar curve.   According to our guidelines we can solve only one question…

Q: Graph the curves having the following polar equations. (a) r² = sin(20). Explain how the curve…

A: (a) Given equation in polar coordinate is Noted that curve is symmetrical about the line ,also…

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…

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.