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4 years ago

8

Neal buys a board game. He pays for the board game and pays \$1.54$1.54dollar sign, 1, point, 54 in sales tax. The sales tax rat

e is 5.5\%5.5%5, point, 5, percent.

1 answer:

jok3333 [9.3K]4 years ago

4 0

You provide info on the circumstances but do not provide instructions. What are you looking for here?

Suppose the board game cost $25 before tax.

If the tax payable was $1.54, then the sales tax rate was r:
$1.54
$25r = $1.54. Solving for r, r = ---------- = 0.0616, or 6.16%
$25

If this isn't quite what you were looking / hoping for, then please ensure you have copied down the original problem exactly.

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4 years ago

Volumes of the solids with disk or shell method?

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The answer to the questions of volumes are given as follows

a) $v=128 \pi$

b) $v=\frac{128}{3} \pi$

c) $v=\frac{1024}{5} \pi$

d) $V=\frac{13568}{15} \pi$

Generally, the questions are mathematically solved below

$y=\sqrt{x}, y=4, x=0$

a) x-axis

if $y=4, x=16, x=0$

Using disk method

$} v=\pi \int_{0}^{16}(\sqrt{x})^{2} d x \\$

$v=\pi\left(\frac{x^{2}}{2}\right)_{0}^{16} \\$

$v=\frac{\pi}{2} \times 16 \times 16 \\$

$v=128 \pi$

b) line y=4

if x=0, y=0 ;

$y=\sqrt{x} \Rightarrow x=y^{2}$

Using shell method

$v = \int_{0}^{4} 2 \pi(4-y) \cdot y^{2} d y \\$

$v=2 \pi \int_{0}^{4}\left(4 y^{2}-y^{3}\right) d y$

$v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\$

$v=\frac{2 \pi}{12}[1024-768] \\$

$v=\frac{512 \pi}{12} \\$

$v=\frac{128}{3} \pi$

c) y-axis

0 ≤ y ≤ 4

x=y^2

Using disk method

volume

$v=\pi \int_{0}^{4} y^{4} d y$$

$v=\pi\left(\frac{y 5}{5}\right)_{0}^{4} \\$

$v=\frac{1024}{5} \pi$

d) line x=-1

y=√x, y=4, x=0

0 ≤ x ≤ 6

Using shell method

volume is

$V=\int_{0}^{16} 2 \pi(1+x) \sqrt{x} d x$$

$V=2 \pi\int_{0}^{16}(x^{1 / 2}+x^{3 / 2}\right) )d x\right. \\$

$V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\$

$V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\$

$V=4 \pi / 3 \cdot 4^{3}+4 \pi / 5 \cdot 4^{5} \\$

$V=4 \pi\left(\frac{1}{3}+\frac{4^{2}}{5}\right)$

$V=\frac{256}{15}(5+48) \pi \\$

$V=\frac{256 \times 53}{15} \pi \\$

$V=\frac{13568}{15} \pi$

Read more about volumes

brainly.com/question/1578538

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