Marksberg radially has a population density of 1000e^−0.01r2 people per km^2, where r is the radius (in km) from the sky river. What is the total population living within 5 km of the sky river?  Please answer it with clear explaination, steps and details. Thank you so much!

A town is of a circular shape. The area of the town is growing with a constant 3 pi mi^2/y(square mile per year). How fast is its radius changing when the radius is exactly 5 miles long?

A hemispherical water tank. shown below has a radius of 6 meters and is losing water. The area of the surface of the water is A=12pih-pih^2 square meters, where h is the depth, in meters, of the water in the tank. When h=3 meters, the depth of the water is decreasing at a rate of -1/2 meters per minute. At that instant, what is the rate at which the area of the water's surface area is decreasing with respect to time?

Use 8 rectangles to find the area of the curve for the equation y = -x^2 + 9 on [-3, 3].

The value of (-1+v3 i)^(1/3)

A rectangular photograph measuring 77 cm by 66 cm is to be displayed in a card mount in a rectangular frame as shown below, with a border of constant width x cm. The owner wants the area of the mount (including the photo) to be 73cm^2.   Find the width x of the border.The border should be ... cm wide (round your answer to three decimal places).