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sweet-ann [11.9K]

3 years ago

13

A pack of cinnamon-scented pencils sells for $7.00. What is the sales tax rate if the total cost of the pencils is $7.21?

2 answers:

Bess [88]3 years ago

7 0

0.21 is the answer ;)

monitta3 years ago

4 0

Answer:

0.21

Step-by-step explanation:

You subtract 7 from 7.21

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Prove that (secx-tanx) = 1-sinx/1+sinx

s2008m [1.1K]

Answer:

you can use reciprocal and quotient formula of trigonometry

4 0

3 years ago

Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs

JulsSmile [24]

Answer:

1) V = 12 π ㏑ 3

2) $\mathbf{V = \dfrac{328 \pi}{9}}$

Step-by-step explanation:

Given that:

the graphs of the equations about each given line is:

$y = \dfrac{6}{x^2}, y =0 , x=1 , x=3$

Using Shell method to determine the required volume,

where;

shell radius = x; &

height of the shell = $\dfrac{6}{x^2}$

∴

Volume V = $\int ^b_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx$

$V = \int ^3_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx$

$V = 12 \pi \int ^3_{x-1} \dfrac{1}{x} \ dx$

$V = 12 \pi ( In \ x ) ^3_{x-1}$

V = 12 π ( ㏑ 3 - ㏑ 1)

V = 12 π ( ㏑ 3 - 0)

V = 12 π ㏑ 3

2) Find the line y=6

Using the disk method here;

where,

Inner radius $r(x) = 6 - \dfrac{6}{x^2}$

outer radius R(x) = 6

Thus, the volume of the solid is as follows:

$V = \int ^3_{x-1} \begin {bmatrix} \pi (6)^2 - \pi ( 6 - \dfrac{6}{x^2})^2 \end {bmatrix} \ dx$

$V = \pi (6)^2 \int ^3_{x-1} \begin {bmatrix} 1 - \pi ( 1 - \dfrac{1}{x^2})^2 \end {bmatrix} \ dx$

$V = 36 \pi \int ^3_{x-1} \begin {bmatrix} 1 - ( 1 + \dfrac{1}{x^4}- \dfrac{2}{x^2}) \end {bmatrix} \ dx$

$V = 36 \pi \int ^3_{x-1} \begin {bmatrix} - \dfrac{1}{x^4}+ \dfrac{2}{x^2} \end {bmatrix} \ dx$

$V = 36 \pi \int ^3_{x-1} \begin {bmatrix} {-x^{-4}}+ 2x^{-2} \end {bmatrix} \ dx$

Recall that:

$\int x^n dx = \dfrac{x^n +1}{n+1}$

Then:

$V = 36 \pi ( -\dfrac{x^{-3}}{-3}+ \dfrac{2x^{-1}}{-1})^3_{x-1}$

$V = 36 \pi ( \dfrac{1}{3x^3}- \dfrac{2}{x})^3_{x-1}$

$V = 36 \pi \begin {bmatrix} ( \dfrac{1}{3(3)^3}- \dfrac{2}{3}) - ( \dfrac{1}{3(1)^3}- \dfrac{2}{1}) \end {bmatrix}$

$V = 36 \pi (\dfrac{82}{81})$

$\mathbf{V = \dfrac{328 \pi}{9}}$

The graph of equation for 1 and 2 is also attached in the file below.

5 0

4 years ago

Fractions 4/16 2/8 15/60 3/9 which fraction is not equivalent to 1/4

BigorU [14]

Answer:

3/9

Step-by-step explanation:

7 0

3 years ago

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If x2 + y2 = 38 and x - y = 2, then what is x? If there are two possible answers, then enter the larger of the two.

Ket [755]

If x-y=2 then x=2+y

And if you insert that in the first equation

$(2 + y) {}^{2} + y {}^{2} = 38$
$4 + 4y + y {}^{2} + {y}^{2} = 38$
$2y {}^{2} + 4y - 34 = 0$
$y = - 1 + \sqrt{17}$
Or
$y = - 1 - \sqrt{17}$

The first one is bigger so the answer is

$y = - 1 - \sqrt{17}$

7 0

3 years ago

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Madeline borrow some money for my friends in order to help my name video game system. Mellana Green payback for friends five dol

Alex

Answer: y=13*5+5

Step-by-step explanation:

4 0

3 years ago

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