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- Determine dimension x to 3 decimal places.If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.How fast is the surface area of a circular oil spill in the ocean changing when the radius is 10ft and the radius is inceasing at 2ft/min?
- Evaluate ∫x3 √(1 - x2) dx using integration by parts.When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.04 cm/min. At what rate is the plate's area increasing when the radius is 56 cm?When a circular plate of metal is heated in a oven, its radius increases at a rate of 0.05 cm/min. at what rate is the plate's area increasing when the radius is 52cm?
- A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing. The length is increasing by 7 in/sec and the width is growing at a rate of 2 in/sec. How fast is the area changing?a gas is escaping a spherical balloon at the rate of 4 cubic centimeters per minute. How fast is the surface area of the balloon shrinking when the radius is 2 centimeters?use integration by parts to solve. ∫ Inx dx