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4 years ago

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Mathematics

1 answer:

Wittaler [7]4 years ago

8 0

The answer for this question is “A”

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The quotient of 6 times a number and 16

Debora [2.8K]

6 times a number = 6n

The quotient of 6 times a number and 16 = 6n / 16

Hope it helps

4 0

4 years ago

Read 2 more answers

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified l

Sloan [31]

Answer:

The integral of the volume is:

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

The result is: $V = 78.97731$

Step-by-step explanation:

Given

Curve: $x^2 + 4y^2 = 4$

About line $x = 2$ --- Missing information

Required

Set up an integral for the volume

$x^2 + 4y^2 = 4$

Make x^2 the subject

$x^2 = 4 - 4y^2$

Square both sides

$x = \sqrt{(4 - 4y^2)$

Factor out 4

$x = \sqrt{4(1 - y^2)$

Split

$x = \sqrt{4} * \sqrt{(1 - y^2)$

$x = \±2 * \sqrt{(1 - y^2)$

$x = \±2 \sqrt{(1 - y^2)$

Split

$x_1 = -2 \sqrt{(1 - y^2)}\ and\ x_2 = 2 \sqrt{(1 - y^2)}$

Rotate about x = 2 implies that:

$r = 2 - x$

So:

$r_1 = 2 - (-2 \sqrt{(1 - y^2)})$

$r_1 = 2 +2 \sqrt{(1 - y^2)}$

$r_2 = 2 - 2 \sqrt{(1 - y^2)}$

Using washer method along the y-axis i.e. integral from 0 to 1.

We have:

$V = 2\pi\int\limits^1_0 {(r_1^2 - r_2^2)} \, dy$

Substitute values for r1 and r2

$V = 2\pi\int\limits^1_0 {(( 2 +2 \sqrt{(1 - y^2)})^2 - ( 2 -2 \sqrt{(1 - y^2)})^2)} \, dy$

Evaluate the squares

$V = 2\pi\int\limits^1_0 {(4 +8 \sqrt{(1 - y^2)} + 4(1 - y^2)) - (4 -8 \sqrt{(1 - y^2)} + 4(1 - y^2))} \, dy$

Remove brackets and collect like terms

$V = 2\pi\int\limits^1_0 {4 - 4 + 8\sqrt{(1 - y^2)} +8 \sqrt{(1 - y^2)}+ 4(1 - y^2) - 4(1 - y^2)} \, dy$

$V = 2\pi\int\limits^1_0 { 16\sqrt{(1 - y^2)} \, dy$

Rewrite as:

$V = 16* 2\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

Using the calculator:

$\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy = \frac{\pi}{4}$

So:

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

$V = 32\pi * \frac{\pi}{4}$

$V =\frac{32\pi^2}{4}$

$V =8\pi^2$

Take:

$\pi = 3.142$

$V = 8* 3.142^2$

$V = 78.97731$ --- approximated

3 0

3 years ago

Mira has breakfast at a restaurant. She leaves a 20% tip of $1.80.

lutik1710 [3]

let's say the breakfast price was "x", so that's the 100%, and we know she gave 20% of that and that is 1.80.

so, 1.80 is 20%, and "x" is the 100%, what is "x"?

$\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 1.80&20\\ x&100 \end{array}\implies \cfrac{1.80}{x}=\cfrac{20}{100}\implies \cfrac{1.8}{x}=\cfrac{1}{5} \\\\\\ 9.0=x\implies 9=x$

3 0

3 years ago

The maximum load of a horizontal beam that is supported at both ends varies jointly as the width and the height and inversely as

dezoksy [38]

Answer:

$360kg$

Explanation:

Here, we want to get the maximum load supported

From the first part of the question, we have it that:

The maximum load g, varies jointly with the width w and the height h, and inversely as the length l between the supports

Mathematically, we have that as:

$g\text{ = k }\times\frac{wh}{l}$

where k is the proportionality constant

Now, let us get the value of k

We substitute the first set of values as follows:

$\begin{gathered} 360\text{ = }\frac{k\times0.1\times0.06}{6} \\ \\ k\text{ = 360,000 }\frac{kg}{m} \end{gathered}$

Now, using this value of k, we want to get the value of g

Mathematically, we have that as:

$g\text{ = }\frac{360,000\times0.2\times0.08}{16}\text{ = 360 }kg$

8 0

1 year ago

2730/10,000 in decimal notation

ziro4ka [17]

2730/10,000 in decimal notation is 0.273

6 0

4 years ago