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3 years ago

If the cube shown is 7 centimeters on all sides what is the length of the diagonal x.

Mathematics

2 answers:

Volgvan3 years ago

7 0

Answer:

9.899

Step-by-step explanation:

7²+7²=98

$\sqrt{98} =9.899$

Marina86 [1]3 years ago

3 0

There's no cube shown but we can guess the diagonal is the long diagonal.

In a rectangular parallelpiped (aka a box) with dimensions a × b × c the long diagonal x satifies a 3D version of the Pythagorean Theorem,

x² = a² + b² + c²

In a cube a=b=c

x² = 3a²

x = a√3

Answer: 7√3

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Can I get help with finding the Fourier cosine series of F(x) = x - x^2

trapecia [35]

Assuming you want the cosine series expansion over an arbitrary symmetric interval $[-L,L]$ , $L\neq0$ , the cosine series is given by

$f_C(x)=\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos nx$

You have

$a_0=\displaystyle\frac1L\int_{-L}^Lf(x)\,\mathrm dx$
$a_0=\dfrac1L\left(\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{x=-L}^{x=L}$
$a_0=\dfrac1L\left(\left(\dfrac{L^2}2-\dfrac{L^3}3\right)-\left(\dfrac{(-L)^2}2-\dfrac{(-L)^3}3\right)\right)$
$a_0=-\dfrac{2L^2}3$

$a_n=\displaystyle\frac1L\int_{-L}^Lf(x)\cos nx\,\mathrm dx$

Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of

$\displaystyle\int(x-x^2)\cos nx\,\mathrm dx=\frac{(1-2x)\cos nx}{n^2}-\dfrac{(2+n^2x-n^2x^2)\sin nx}{n^3}$

and so

$a_n=-\dfrac{4L\cos nL}{n^2}+\dfrac{(4-2n^2L^2)\sin nL}{n^3}$

So the cosine series for $f(x)$ periodic over an interval $[-L,L]$ is

$f_C(x)=-\dfrac{L^2}3+\displaystyle\sum_{n\ge1}\left(-\dfrac{4L\cos nL}{n^2L}+\dfrac{(4-2n^2L^2)\sin nL}{n^3L}\right)\cos nx$

4 0

3 years ago

The slope of the line that passes through the points (-1,w) and (-10,4) is 1/9

forsale [732]

Answer:

Step-by-step explanation:

5 0

2 years ago

Slope for the line perpendicular to the line shown in the graph

Flauer [41]

It would be positive 1/3 because if you move to the right one on your bottom point and up 3 it gives you +1/3

8 0

3 years ago

kevin's garden is rectangular and measures 12 metres by 15 metres. He plans to lay new turf in the garden which will cost £8 per

DedPeter [7]

Answer:

Kevin’s garden is rectangular and measures 12 metres by 15 metres. He plans to lay new turf in the garden which will cost £8 per square metre. How much turf will he need to buy and how much will this cost? 4)Inga needs to buy enough skirting board to replace the old skirting board in her bedroom. The bedroom is 5m 20cm long and 4m 80cm wide.

Step-by-step explanation:

6 0

3 years ago

The figure of Circle A shown below has diameter PR which intersects QS at point B and the measurements shown. Calculate the foll

nata0808 [166]

The figure is an illustration of the relationship between the angles in a circle and arc

<h3>The measure of angle PSQ</h3>

From the figure, the arc PQ is subtended by the angle PAQ.

This means that:

PQ = ∠PAQ

Given that ∠PAQ = 130, it means that:

Arc PQ = 130

The measure of PSQ is then calculated using:

∠PSQ = 0.5 * Arc PQ ----- inscribed angle is half a subtended angle.

This gives

∠PSQ = 0.5 * 130

∠PSQ = 65

Hence, the measure of ∠PSQ is 65 degrees

<h3>The measure of arc QR</h3>

A semicircle measures 180 degrees.

This means that:

QR + PQ = 180

So, we have:

QR = 180 - PQ

Substitute 130 for PQ

QR = 180 - 130

QR = 50

Hence, the measure of QR is 50 degrees

<h3>The measure of arc RS</h3>

The measure of arc RS is then calculated using:

∠RPS = 0.5 * Arc RS ----- inscribed angle is half a subtended angle.

Where ∠RPS = 35

So, we have:

35 = 0.5 * Arc RS

Multiply both sides by 2

Arc RS = 70

Hence, the measure of RS is 70 degrees

<h3>The measure of angle AQS</h3>

In (a), we have:

∠PSQ = 65

This means that:

∠PSQ = ∠PSB = 65

So, we have:

∠PSB = 65

Next, calculate SBP using:

∠SBP + ∠BPS + ∠PSB = 180 ---- sum of angles in a triangle.

So, we have:

∠SBP + 35 + 65 = 180

∠SBP + 100 = 180

This gives

∠SBP = 80

The measure of AQS is then calculated using:

AQS = AQB = 180 - (180 - SBP) - (180 - PAQ)

This gives

AQS = 180 - (180 - 80) - (180 - 130)

Evaluate

AQS = 30

Hence, the measure of AQS is 30 degrees

<h3>The measure of arc PS</h3>

A semicircle measures 180 degrees.

This means that:

PS + RS = 180

This gives

PS = 180 - RS

Where RS = 70

So, we have:

PS = 180 - 70

Evaluate

PS = 110

Hence, the measure of arc PS is 110 degrees

Read more about circles and arcs at:

brainly.com/question/15096899

#SPJ1

6 0

2 years ago