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Area of a Polar Region In Exercises $1-4,$ write an integral that represents the area of the shaded region of the figure. Do not evaluate the integral.$$r=4 \sin \theta$$
Area of a Polar Region In Exercises $1-4,$ write an integral that represents the area of the shaded region of the figure. Do not evaluate the integral.$$r=\cos 2 \theta$$
Area of a Polar Region In Exercises $1-4,$ write an integral that represents the area of the shaded region of the figure. Do not evaluate the integral.$$r=3-2 \sin \theta$$
Area of a Polar Region In Exercises $1-4,$ write an integral that represents the area of the shaded region of the figure. Do not evaluate the integral.$$r=1-\cos 2 \theta$$
Writing Consider the polar equation $r=\frac{4}{1+e \sin \theta}$.(a) Use a graphing utility to graph the equation for $e=0.1$ $e=0.25, e=0.5, e=0.75,$ and $e=0.9 .$ Identify the conic and discuss the change in its shape as $e \rightarrow 1^{-}$ and $e \rightarrow 0^{+}$(b) Use a graphing utility to graph the equation for $e=1$ Identify the conic.(c) Use a graphing utility to graph the equation for $e=1.1$ $e=1.5,$ and $e=2 .$ Identify the conic and discuss the change in its shape as $e \rightarrow 1^{+}$ and $e \rightarrow \infty$
Finding the Area of a Polar Region In Exercises $5-16$ , find the area of the region.Interior of $r=6 \sin \theta$
A total of 60 kids were asked which movie they liked. 24 said they liked Aladdin; 48 said they liked Beauty and the Beast. How many in total liked only Beauty and the Beast?..
Find the component of u along v.u = 6i - 25j, v = j
A toy car mass 0.03kg, on a ramp with no friction, begins at 0.6 meters high. At the bottom it collides in elastically with a toy truck mass 0.3 kg, at rest. After the collision the car is at rest, what is the final velocity of the truck?
A package slides down a ramp 14 meters high, and at the bottom hits a rough patch with friction (u= 0.07). How far will it slide, before it comes to a stop?
A hollow ball, rolls down a hill that is 7 meters high. What is the velocity at the bottom of the hill?
As a safety device large springs are installed under elevators. If an elevator of 1,205 kg is falling from a height of 28 meters. How large must the Spring Constant be to safely stop the elevator in 1.5 meters.