Arc Length in Polar Coordinates dx' L = Remember: dt dt dt x =r cose For polar graphs: y =r sin 0 If we find derivatives and plug them into the formula, we (eventually) get: Length = {" * +() dr de

Q: 3. Find the cartesian equation of r cos 0 = -4 and identify its graph.

A: To find the Cartesian equation of rcosθ=-4 and identify its graph. Solution: In Cartesian…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 1. For the equation 3x² + 4xy = 16 eliminate the xy term by…

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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: 4. A straight river flows north at a speed of 3 mi/h. A boater attempting to cross the river heads…

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Q: 2. The moment the batmobile passes through the point (-1, /3), the angle 0 is changing at a rate…

A: We know y=2sin θ Differentiate y with respect to t: dydt=2cos θdθdt As the point 2, 2 is in I…

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: • Question 1. Given the point R (1,4) outside the circle L = x2 + y2 -2y = 1 x² + y2 - 2y - 1 = 0…

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Q: Find the slope of the tangent line to the polar curve r = sin(70) at 0=. Enter as an integer or…

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Q: Sketch the graph of the curve with the polar equation: r=2– sin(20).

A: To draw a polar graph we need to check its symmetricity by using following   #  In the first test,…

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

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Q: Problem 4 Parts A, B, and C

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Q: 4. A biologist collects data on a population of rabbits as indicated below. A B C D EFGH Time…

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Q: If you are given parametric equations of a curve, what is the formula for finding its arclength?…

A: To write the arc length formula for the given types of curves.

Q: Part A, B, and C

A: According to the given information it is required to sketch the graph of the given polar equation.…

Q: Suppose the point (4,6) sits on a ray from the origin making an angle of A in standard position, and…

A: topic - trigonometric ratios

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: 3. 65. r = -2 66. r= sin 0 Cos e 67. r 3 sec 0 68. r = 2 csc 0 69. r = 5 70. r= -3 71. 0 72. 0 = 0…

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Q: 60 50 60 50 40 40 30 30 20 10 20 50 100 150 10 20 40 60 80 (d) Use a graphing utility to approximate…

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Q: 4. Determine the sine and cosine equations in degrees for the graph below. (0, 1) (360, 1) 30 90 120…

A: We have to find the equation of sine and cosine.

Q: Convert the rectangular coordinate point (2,-2) to polar coordinate.

A: To convert into polar coordinates

Q: 3. As cars travel on gravel roads, the roads erode and take on a "washboard" look due to the…

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Q: Find a Cartesian equation whose graph is the same as that of the polar equa- 1² cos 20 and (hence or…

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Q: 2. Part 2 - Find the error(s) and solve the problem correctly. Convert the polar equation to…

A: r=-4cosθ

Q: PLEASE PLEASE DRAW THE GRAPH!!!!!!!   solve only 3

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Q: Suppose you graph the function r(0) = 4cos (20) on the interval [0,2π] in polar coordinates. How…

A: Any point in the polar coordinate system is represented using the ordered pair: r, θ. At the origin,…

Q: For the polar function r (0) = 2 + 3 sin do the following: 1. Create a table of values for 8 [0, 2π]…

A: The given curve has the polar equation: rθ=3 cos2θ. Consider the following angles and respective…

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…