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2 years ago

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(2.437×10⁴)(6.5411 x 10^9)/(5.37x10^6). write in scientific notation

1 answer:

Musya8 [376]2 years ago

4 0

Answer:

the answee is

2.968456 ×10^7

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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

1 year ago

Read 2 more answers

Which process enables the boy to see over the wall?

den301095 [7]

Answer: yeah it is reflection

6 0

2 years ago

During which month is the bacteria population just under 1 million?

Thepotemich [5.8K]

D. March because it is just below the 1 million marker on the graph and it is the only one that low.

5 0

2 years ago

If Sarah melts 10g of tin. What mass of melted tin would she have at the end of the experiment?

Nastasia [14]

Answer:

10g

Explanation:

As the Law of Conservation of Mass states that " Mass can neither be created nor be destroyed in a chemical reaction".

Though melting of tin isn't a chemical change, the same logic is applied here...

Hence,

The mass of tin will be 10 g itself...

7 0

2 years ago

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The cable holding a 2125 kg elevator has a maximum strength of 21,750 N. What is the maximum upward acceleration the cable can g

vivado [14]

Answer:

10.23m/s^2

Explanation:

GIven data

mass of elevator = 2125 kg

Force= 21,750 N

Required

The maximum acceleration upward

F= ma

a= F/m

a=21,750/2125

a= 10.23m/s^2

Hence the acceleration is 10.23m/s^2

4 0

2 years ago