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(a) A model for the shape of a bird’s egg is obtained by rotating about the x-axis the region under the graph of
Use a CAS to find the volume of such an egg.
(b) For a red-throated loon,
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- Find c> (such that the area of the region enclosed by the parabolas y = x² - c² and y = c²x² is 1944. (a) The curves intersect when x is . (Put the smaller one first.) (b) The area of the region (as a function of C) is (c) To get the area 1944, we take C = andarrow_forwardConsider the graph of the function y(x) = 3. a) Between 0 < x < L, the graph defines a region below the graph and above the x-axis What is the area of this region? b) Create a formula, A(L), for the area under the graph of y(x) between 0 and L. c) Graph A(L).arrow_forwardA new exhibit hall at a convention center has a floor bounded by x 0, x= 100, y= - 100 +0.01x, and y= 100 - 0.01x. The ceiling lies on the graph of C(x,y) = 25-0.09x. (Each unit on the x, y, and z axes represents one foot.) Find the volume of the exhibit hall (in cubic feet). The volume of the exhibit hall is (Simplify your answer.) cubic feet.arrow_forward
- A concrete reservoir in the shape of a triangular prism is being filled with water at the constant rate of 2 cubic feet per minute. The reservoir is 4 feet deep, measures 6 feet across the top, and is 20 feet long (see figure). For any time t>=0, let H represent the depth of the water in the reservoir and let W represent the width of the rectangular region of water at the top. a. If the reservoir is initially empty, how long will it take to fill completely? b. How fast is the depth of the water in the reservoir changing when the reservoir is half-full? Remember to includes units. c. How fast is the rectangular area of the surface of the water changing when the reservoir is half full? Indicate units of measure.arrow_forwarda) Estimate the area under the graph of f(x) = 7 + 4x2 from x = −1 to x = 2 using three rectangles and right endpoints. R3 = R6 = Sketch the curve and the approximating rectangles for R3 Sketch the curve and the approximating rectangles for R6. (b) Repeat part (a) using left endpoints. L3 = L6 = Sketch the curve and the approximating rectangles for L3. Sketch the curve and the approximating rectangles for L6. (c) Repeat part (a) using midpoints. M3 = M6 = Sketch the curve and the approximating rectangles for M3. Sketch the curve and the approximating rectangles for M6. (d) From your sketches in parts (a)-(c), which appears to be the best estimate?arrow_forwarda=4 b=4 c=5arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage