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Find the area of the specified region.Inside one leaf of the four-leaved rose r = 3 sin 2θ

Find the slope of the polar curve at the indicated point.r = 5 cos 3θ, θ = 

Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle’s path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion.x = 4 cos t, y = 4 sin t, π ≤ t ≤ 2π

Replace the polar equation with an equivalent Cartesian equation. 3r cos θ + 5r sin θ = 1

Express the number as the ratio of two integers.0.77777 . . .

Find a formula for the nth term of the sequence.-1, 1, 3, 5, 7 (every other integer starting with -1)

Find a formula for the nth term of the sequence.0, , 0, , 0 (alternating 0’s and ‘s)

Find the slope of the polar curve at the indicated point.r = 8 cos 3θ, θ = 

Find the limit of the sequence if it converges; otherwise indicate divergence.an = 9 + (0.3)n

Solve the problem.Mari drops a ball from a height of 16 meters and notices that on each bounce the ball returns to about  of its previous height. About how far will ball travel before it comes to rest?