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10. [0.35/0.5 Points] DETAILS SCALCET8 3.9.026.MI.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A trough is 14 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 10 ft3/min, how fast is the water level rising when the water is 8 inches deep? Step 1 Let h be the water's height and b be the distance across the top of the water. Using the diagram below, find the relation between b and h. b h H|W h PREVIOUS ANSWERS
Step 2 The volume of the water is as follows. V = bhl = bh (14✔ 14 = (3h)(h) = 21h² Step 3 We must find dh/dt. We have 10 = dv dt = 42h Step 4 In feet, we know that h = Submit Skip (you cannot come back) 21h² 42h dh dt Enter a fraction, integer, or exact decimal. Do not approximate.
Step 5 Consequently, we can conclude the following. dh dt = 4/8 X ft/min Submit Skip (you cannot come back)