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Modeling Data The circumference C (in inches) of a vase is measured at three-inch intervals starting at its base. The measurements are shown in the table, where y is the vertical distance in inches from the base.
y |
0 |
3 |
6 |
9 |
12 |
15 |
18 |
C |
50 |
65.5 |
70 |
66 |
58 |
51 |
48 |
(a) Use the data to approximate the volume of the vase by summing the volumes of approximating disks.
(b) Use the data to approximate the outside surface area (excluding the base) of the vase by summing the outside surface areas of approximating frustums of right circular cones.
(c) Use the regression capabilities of a graphing utility to find a cubic model for the points (y, r), where
(d) Use the model in part (c) and the integration capabilities of a graphing utility to approximate the volume and outside surface area of the vase. Compare the results with your answers in parts (a) and (b).
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Chapter 7 Solutions
Bundle: Calculus, 10th + WebAssign Printed Access Card for Larson/Edwards' Calculus, 10th Edition, Multi-Term
- Find all values of x for the given function where the tangent line is horizontal. 3 =√x³-12x² + 45x+5arrow_forwardFind the equation of the tangent line to the graph of the given function at the given value of x. 6 f(x) = x(x² - 4x+5)*; x=2arrow_forwardFind the equation of the tangent line to the graph of the given function at the given value of x. f(x)=√√x+33; x=4arrow_forward
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