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Show all work using implicit differentiation for related rates:
A 13-foot ladder is leaning against a house when its base starts to slide away. By the time the base is 12 feet from the house, the base of the ladder is moving at the rate of 5 ft/sec.
At what rate is the area of the triangle formed by the ladder, wall, and ground changing at that time? Use A=1/2(b)(h)
Suppose three fair coins are flipped. Find the probability for each of the following events. Exactly two coins are tails.
The bus driver said, "We have gone 33 miles so far. If we continue to travel at the same rate, how many more minutes until we arrive?"
(c) If its weekly cost function is C(x) = 68000 + 150x, how should the manufacturer set the size of the rebate in order to maximize its prot?
Royal Palm hospital has 500 beds and 55 bassinets. As the HIM manager, you report monthly statical data of hospital operations to administration and department managers. Use the information in table 3-3 to calculate the percentage of occupancy for..
A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.
you are going to create a problem involving one of the shapes you are learning about in this unit. choose one of the
A circular swimming pool has a diameter of 25 ft, the sides are 6 ft high, and the depth of the water is 5 ft. How much work is required to pump all of the water over the side? (Use the fact that water weighs 62.5 lb/ft3.)
Integration by parts method - How much longer would the worm be at t = 2, if it always grew at the maximum rate? Use Integration by parts.
The minute hand on a watch is 5 mm long and the hour hand is 4 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)
How fast is the area of the rectangle changing when the width is 10 cm and the height is 15 cm? Is the area decreasing or increasing?
A cyclist travels 105 km in 7 hours going against the wind. He travels 133 km with the wind in the same amount of time. What is the rate of the cyclist in still air and what is the rate of the wind?
Given a = 9i - 5j and b = 7i-4j, express i and j in terms of a and b. Given a= and b = determine whether a and b are parrallel, perpendicular, or neither.
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