What would be an equation and answer to the equation for The product of 6 and 3 more than k is 48

Mathematics

1 answer:

My name is Ann [436]3 years ago

7 0

You know what product means right? (+,-,×,÷)

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lina2011 [118]

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3 years ago

Find the volume of the solid formed by rotating the region bounded by the given curves about the indicated axis. Y = 1x, y = 1,

Goryan [66]

The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.

Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is

π (radius) (height) = π (1/y)² ∆y = π/y² ∆y

and the volume of a stack of n such disks is

$\displaystyle V_n = \sum_{i=1}^n \pi {y_i}^2 \Delta y$

where $y_i$ is a point sampled from the interval [1, 5].

As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,

$\displaystyle V = \lim_{n\to\infty} V_n = \int_1^5 \frac{\pi}{y^2} \, dy$