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If the 0.145 mm diameter tungsten filament in a light bulb is to have a resistance of 0.161 Ω at 20.0°C, how long should it be? The resistivity of tungsten at 20.0°C is 5.60 10-8 Ω · m

diameteter (d) = 0.145 mm,

resistance (R) = 0.161 Ω,

resistivity (ρ) = 5.60 *10-8 Ω · m

$$\rho = \dfrac{RA}{L} \qquad \rm{A} = \dfrac{\pi\ d^2}{4} \\\\
\text{Length (L): } \qquad
\boxed{L=\dfrac{\pi\ d^2 }{4} \dfrac{R}{\rho}}$$

$$\small{\text{
$
L= \left(
\dfrac{ \pi * 0.145^2 *0.161 } { 4 * 5.60 \cdot 10^{-8} }
\right)
\left( \dfrac{mm^2\ \Omega}{\Omega\ m}
\right)
$
}}
\qquad \boxed{
1\, \dfrac{\Omega\ mm^2}{m} = 10^{-6}\ \Omega\ m \qquad
1\ \Omega\ m = \dfrac{10^6\ mm^2\ \Omega}{m}
}\\\\
\small{\text{
$
L= \left(
\dfrac{ \pi * 0.145^2 *0.161 } { 4 * 5.60 \cdot 10^{-8} }
\right)
\left( \dfrac{mm^2\ \Omega}{\dfrac{10^6\ mm^2\ \Omega}{m}}
\right)
$
}}\\\\\\
\small{\text{
$
L= \left(
\dfrac{ \pi * 0.145^2 *0.161 } { 4 * 5.60 \cdot 10^{-8} }
\right)
\left( \dfrac{m}{10^6}
\right)
$
}}\\\\\\
\small{\text{
$
L= \left(
\dfrac{ \pi * 0.145^2 *0.161 } { 4 * 5.60 \cdot 10^{-2} }
\right)
\ m
$
}}\\\\
\small{\text{
$
L=\dfrac{ \pi * 0.145^2 *0.161 \cdot 10^2} { 4 * 5.60 } \ m
$
}}\\\\
\small{\text{
$
L=0.04747486461 \ m
$
}}\\
\small{\text{
$
L=4.747486461 \ cm \approx 4.75 \ cm
$
}}$$

126,562,500

Percent means "per hundred". 5.5 % means 5.5/100 = 0.055

"5.5% of something" means "5.5% * something"

The sales tax is: 5.5% * 25 350 = 0.055 * 25 350 = <your answer>

Total cost = 25 350 + sales tax = <your answer>

13,500=

75,000*18%= 13,500

a shopkeeper marks his goods 40% above the cost price and then allows adiscount of 20%.find how much will a customer pay for an article which costs shopkeeper rs.200 and a sales tax of 10% is levied on the sale price of the article.give your answer correct to the nearest rupee.

Well.....let's take this in steps.....if he buys it for 200 and then has a 40% markup, the regular price will be 200 x 1.4  = 280

A 20% discount on this will result in a sales price of 280 x .80  = 224

And a 10% tax on this  =  224 x 1.1  = 246.4 = 246 rupees (rounded)

40%/100%=0.4

0.4*300,000=120,000

All you have to do is change the caculator to the angle version that's on the bottom left corner.

i dont feel like drinking water but ok i'll try!

thanks!

Drink lots of water, dehaydration can cause severe headache.  Codeine works better than asprin for a headache.  It is ususally combined with asprin or with paracetamol.

How can i get the sum of interior angles of any polygon ?

The sum of interior angles of a 3 Point polygon = 1 ( triangle )  =   $$1*\pi$$

The sum of interior angles of a 4 Point polygon = 2 ( triangle )  =   $$2*\pi$$

The sum of interior angles of a 5 Point polygon = 3 ( triangle )  =   $$3*\pi$$

The sum of interior angles of a 6 Point polygon = 4 ( triangle )  =   $$4*\pi$$

$$\dots$$

The sum of interior angles of a n Point polygon = n-2 ( triangle )  =   $$\qquad\small{\text{$ (n-2)*\pi \quad $ or $ \quad (n-2)* 180 \ensurement{^{\circ}} $
}}$$

different polygons have different sums....which one do you want?

i did...lied for 3hours but now i woke...still a headache!

Take a couple of aspirin......lie down for about an hour, or so......you should feel better...

Thanks Alan :)

Yes, nice work, thank you :)))

Very impressive, Alan....!!!

Perhaps for a not yet afflicted youth it is wise to isolate oneself from the curse that afflicts the land.  For youth be very volnerable to this great pestilence.  Even the name must be spoken in the most hushed tones lest the evil hears its name and crosses the hearth to enter and corrupt the home of the unguarded youth.

But this be not thee Chuirgeon Tud.  Thou be a great man of medicine.  Thine magick shall encompass thee and keep thee within a powerful protective cloak.  Tis thine sworn oath to protect those in weakened condition. 

Yes this ignorant man with poison in his veins should not have encouraged or allowed  the intervention of these ignorant afflicted witches.  However thee be not he.  Thou knowledge is strong protection.  Thee can walk among these people and be not corrupted.  Thine knowledge make thee impervious to this infection.  Only the fire water that thee so cherishes could make thee fall into the clutches of those infected with the scourge of this contagious darkness disease.  So, my dear Tud, thee should pull thineself up and go forth to fight your foe.  Wisdom and knowledge be thine powerful weapons.

I am however entranced.  I wish to stand on the planet of war and watch the Earth pass before the sun.   Or perhaps to stand upon the northern pole and watch the magical lights dance in sky above my head.  These be wonderments to behold.

Yes If thee can make this happen then those with pestilence can wait a little longer for the touch of thine magical hands.

Queen Guinevere,

Sovereign of the Great and Magical Land of Camelot.

.

It is 7,500.... 300,000/40 = 7,500

My Goodness Takahiro, I could fill my swimming pool with your tears :)

Tues 10/2/15

@@ End of Day Wrap   Mon 9/2/15   Sydney, Australia   Time 9:20 pm ♪ ♫

Hi all,

The last two days our wonderful answerers have been Nauseated, Alan, Sasini, CPhill, Heureka, Dragonlance, Mathematicians, Tetration, SoulReaper22, BrittanyJ, geno3141, GoldenLeaf, saseflower, Rosala and TakahiroMaeda.  Thank you. 

DragonSlayer paid us a quick visit which we were thrilled about.  Thanks DS, visit whenever you can, we all miss you.  DS gave us the address of a practice and explain site that does look very good.  Thanks Dragon.   

one over two plus one over four plus one over eight

$$\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8} = ?\\\\
\boxed{
\dfrac{1}{2} = 2 * \left(\dfrac{1}{4} \right) \qquad
\dfrac{1}{4} = 2 * \left(\dfrac{1}{8} \right) }\\\\
\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8} =
2*2* \left(\dfrac{1}{8}\right) + 2 * \left(\dfrac{1}{8}\right) +\left(\dfrac{1}{8}\right) = \left(\dfrac{1}{8}\right) \left(4+2+1\right) = \dfrac{7}{8}$$

If it takes 4 years for $2000 to accumulate to $4000, find the compound interest rate

Assuming that it is compounding yearly

4000=2000(1+r)^4

2=(1+r)^4

2^(1/4)=1+r

2^0.25   -1=r

$${{\mathtt{2}}}^{{\mathtt{0.25}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{0.189\: \!207\: \!115\: \!002\: \!721\: \!1}}$$

rate is 18.9%