20 4. An ant walks on a flat surface along a curve with polar equation r= from a point where 0=0 to another point where 0= 27 rad. (a) Calculate the values of r for 0 equals to 0,. 7. 3 and 27 radians, and hence make a sketch of the trajectory of the ant. (b) Determine the total distance travelled by the ant.

Q: 3. A plane flies 80 km S 50° E * and after a brief stopover flies 45 km S 25° W. Determine the…

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Q: Find the points (x, y) at which the polar curve 8 cos 0, horizontal tangent line. Vertical Tangent…

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Q: Convert the cartesian coordinate (-6, – 1) to polar coordinates, 0 < 27

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Q: Show that the curve r= sin(0) tan() (called a cissoid of Diocles) has the line x = 1 as a vertical…

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Q: Using the polar function r = 1 + cos(θ), find the slope of the tangent line at the point (3/2, pi/3)

A: Given: The polar function is, r=1+cosθ

Q: Find the slope of the polar curve r = 2( 1 – cosx ) when x = pi/4 . a. 1.707 b. 2.414 c. 1.866 d.…

A: Given equation of curve : r=21-cosx   ,  x=π4. drdx=2sinx The slope of polar curve   r=21-cosx  at…

Q: 9. Sketch the polar curves r = 5sine and r = 5 sin(30) on the same grid below.

A: The given polar curves are  r=5sin(θ)r=5sin(3θ)

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: Consider the polar curve given by the equation r(0) = 1 - sin(30). It is an example of what is…

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Q: 2.) Given the parametric equations x=cos3t and y=sin3t. Find the equation of the normal line at the…

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

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

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Q: Given polar curve r = −6 sin(θ) do the following. (a) Find the Cartesian equation for this curve.…

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