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4 years ago

Is fire actually hot and why do we call it hot; is it a classification for when something burns you.

Physics

1 answer:

rodikova [14]4 years ago

6 0

Yes it is classified as hot

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State and prove bessel inequality

maria [59]

Statement :- We assume the orthagonal sequence ${{\{\phi\}}_{1}^{\infty}}$ in Hilbert space, now ${\forall \sf \:v\in \mathbb{V}}$ , the Fourier coefficients are given by:

${\quad \qquad \longrightarrow \sf a_{i}=(v,{\phi}_{i})}$

Then Bessel's inequality give us:

${\boxed{\displaystyle \bf \sum_{1}^{\infty}\vert a_{i}\vert^{2}\leqslant \Vert v\Vert^{2}}}$

Proof :- We assume the following equation is true

${\quad \qquad \longrightarrow \displaystyle \sf v_{n}=\sum_{i=1}^{n}a_{i}{\phi}_{i}}$

So that, ${\bf v_n}$ is projection of ${\bf v}$ onto the surface by the first ${\bf n}$ of the ${\bf \phi_{i}}$ . For any event, ${\sf (v-v_{n})\perp v_{n}}$

Now, by Pythagoras theorem:

${:\implies \quad \sf \Vert v\Vert^{2}=\Vert v-v_{n}\Vert^{2}+\Vert v_{n}\Vert^{2}}$

${:\implies \quad \displaystyle \sf ||v||^{2}=\Vert v-v_{n}\Vert^{2}+\sum_{i=1}^{n}\vert a_{i}\vert^{2}}$

Now, we can deduce that from the above equation that;

${:\implies \quad \displaystyle \sf \sum_{i=1}^{n}\vert a_{i} \vert^{2}\leqslant \Vert v\Vert^{2}}$

For ${\sf n\to \infty}$ , we have

${:\implies \quad \boxed{\displaystyle \bf \sum_{1}^{\infty}\vert a_{i}\vert^{2}\leqslant \Vert v\Vert^{2}}}$

Hence, Proved

5 0

2 years ago

Read 2 more answers

How quickly a leaf grows is proportional how big [ie the surface area] the leaf is. If the area of the leaf grows from 2cm2 to 3

marusya05 [52]

Answer: 9 days

Explanation:

Step 1

Let the rate of Leaf growth r be defined as, $\frac{Increase in area}{time taken}$ = $\frac{A1 - A}{t}$

where A is initial area of the leaf, A1 is the final area of the leaf and t is the time taken for the increase in Area.

Express the proportional relationship in equation.

Given that rate of leaf growth, r is proportional to the surface area of the leaf A. we have r ∝ A.

r = kA, where k is the rate constant.

therefore, k = $\frac{r}{A}$

when A = 2 $cm^{2}$ , A1 = 3

so k = $\frac{\frac{3 - 2}{3}}{2}$

= $\frac{1}{3}$ ÷ 2

= 0.33 ÷ 2

k = 0.167

After calculating the rate constant k, we then find the time t when A1 is 5 $cm^{2}$

we have r = k × A1 = $\frac{A1 - A}{t}$

so, 0.167 × 2 = $\frac{5 - 2}{t}$

0.33 = $\frac{3}{t}$ .

t = 3/0.33

Therefore, t = 9 days.

3 0

4 years ago

An airplane starts at rest and accelerates at 6.8 m/s2 at an angle of 39° south of west. After 9 s, how far in the westerly dire

cestrela7 [59]

Answer:36.8

Explanation:

7 0

4 years ago

An ice cube of mass 50.0 g can slide without friction up and down a 25.0 degree slope. The ice cube is pressed against a spring

BlackZzzverrR [31]

Answer:

a) $s = 0.603\,m$ , b) $s = 2.412\,m$

Explanation:

a) The system ice cube-spring is modelled by means of the Principle of Energy Conservation. Let assume that height at the bottom is zero:

$U_{g} = U_{k}$

$m\cdot g \cdot s\cdot \sin \theta = \frac{1}{2}\cdot k \cdot x^{2}$

$s = \frac{k\cdot x^{2}}{2\cdot m\cdot g \cdot \sin \theta}$

$s = \frac{(25\,\frac{N}{m} )\cdot (0.1\,m)^{2}}{2\cdot (0.05\,kg)\cdot (9.807\,\frac{m}{s^{2}} )\cdot \sin 25^{\textdegree}}$

$s = 0.603\,m$

b) The distance travelled by the ice cube is:

$s = \frac{(25\,\frac{N}{m} )\cdot (0.2\,m)^{2}}{2\cdot (0.05\,kg)\cdot (9.807\,\frac{m}{s^{2}} )\cdot \sin 25^{\textdegree}}$

$s = 2.412\,m$

7 0

3 years ago

Read 2 more answers

A bird flies from the South Pole to the North Pole. Part of the journey is 1000 miles that takes 2 weeks. What is the bird’s vel

viktelen [127]

1000 miles = 1610km = 1.61x10^6m
2 weeks = 14 days = 14x24x1440

V=d/t = 1.61x10^6/14x24x1440
= 3.33m/s

6 0

3 years ago

Read 2 more answers