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Chapter 6: Q. 26 (page 556)

The mass of the solid of revolution obtained by rotating the graph of y = 4.5 鈭� 0.5 $x^{2}$ on [0, 3] around the y-axis and whose density at height y is 蚁( y) = 1.3 鈭� 0.233y ounces per cubic inch.

Short Answer

Expert verified

$6 蟺$

Step by step solution

Step1. Given Information

Equation of graph,

$y = 4.5 - 0.5 x^{2}$

Equation of density,

$蚁 (y) = 1.3 - 0.233 y$

Step2. Calculate

$M = {鈭�}_{0}^{2 蟺} {鈭�}_{0}^{蟺} {鈭�}_{1}^{2} 蚁 \sin 蠒 d 蚁 d 蠒 d 胃鈭� \frac{3}{2} \sin 蠒 d 蠒 d 胃 = 3 鈭� d 胃 = 6 蟺$

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In the process of solving $\frac{d y}{d x} = y$ by separation of variables, we obtain the equation $| y | = e^{x + C}$ . After solving for $y$ , this equation becomes $y = A e^{x}$ . How is $A$ related to $C$ ? What happened to the absolute value?

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The mass of the solid of revolution obtained by rotating the graph of y = 4.5 鈭� 0.5x2 on [0, 3] around the y-axis and whose density at height y is 蚁( y) = 1.3 鈭� 0.233y ounces per cubic inch.

Short Answer

Step by step solution

Step1. Given Information

Step2. Calculate

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The mass of the solid of revolution obtained by rotating the graph of y = 4.5 鈭� 0.5 $x^{2}$ on [0, 3] around the y-axis and whose density at height y is 蚁( y) = 1.3 鈭� 0.233y ounces per cubic inch.