<span>Exactly 4(4 - 2*2^(1/3) + 2^(2/3)) feet,
or approximately 12.27023581 feet.
Let's first create an equation to calculate the relative intensity of the light based upon the distance D from the brighter light source. The distance from the dimmer light source will of course be (20-D). So the equation will be:
B = 4/D^2 + 1/(20-D)^2
The minimum and maximum can only occur at those points where the slope of the equation is 0. And you can determine the slope by using the first derivative. So let's calculate the first derivative.
B = 4/D^2 + 1/(20-D)^2
B' = d/dD [ 4/D^2 + 1/(20-D)^2 ]
B' = 4 * d/dD [ 1/D^2 ] + d/dD [ 1/(20-D)^2 ]
B' = 4(-2)D^(-3) + (-2)(20 - D)^(-3) * d/dD [ 20-D ]
B' = -8/D^3 - 2( d/dD [ 20 ] - d/dD [ D ] )/(20 - D)^3
B' = -8/D^3 - 2(0 - 1)/(20 - D)^3
B' = 2/(20 - D)^3 - 8/D^3
Now let's find a zero.
B' = 2/(20 - D)^3 - 8/D^3
0 = 2/(20 - D)^3 - 8/D^3
0 = 2D^3/(D^3(20 - D)^3) - 8(20 - D)^3/(D^3(20 - D)^3)
0 = (2D^3 - 8(20 - D)^3)/(D^3(20 - D)^3)
0 = 2D^3 - 8(20 - D)^3
8(20 - D)^3 = 2D^3
4(20 - D)^3 = D^3
4(8000 - 1200D + 60D^2 - D^3) = D^3
32000 - 4800D + 240D^2 - 4D^3 = D^3
32000 - 4800D + 240D^2 - 5D^3 = 0
6400 - 960D + 48D^2 - D^3 = 0
-6400 + 960D - 48D^2 + D^3 = 0
D^3 - 48D^2 + 960D - 6400 = 0
We now have a simple cubic equation that we can use the cubic formulas to solve.
Q = (3*960 - (-48)^2)/9 = 64
R = (9*(-48)*960 - 27*(-6400) - 2*(-48)^3)/54 = -384
D = Q^3 + R^2 = 64^3 + (-384)^2 = 409600
Since the value D is positive, there are 2 imaginary and 1 real root. We're only interested in the real root.
S = cbrt(-384 + sqrt(409600))
S = cbrt(-384 + 640)
S = cbrt(256)
S = 4cbrt(4)
T = cbrt(-384 - sqrt(409600))
T = cbrt(-384 - 640)
T = cbrt(-1024)
T = -8cbrt(2)
The root will be 4cbrt(4) - 8cbrt(2) + 48/3
So simplify
4cbrt(4) - 8cbrt(2) + 48/3
=4cbrt(4) - 8cbrt(2) + 16
=4(cbrt(4) - 2cbrt(2) + 4)
= 4(4 - 2*2^(1/3) + 2^(2/3))
Which is approximately 12.27023581
This result surprises me. I would expect the minimum to happen where the intensity of both light sources match which would be at a distance of 2/3 * 20 = 13.3333 from the brighter light source. Let's verify the calculated value.
Using the brightness equation at the top we have:
B = 4/D^2 + 1/(20-D)^2
Using the calculated value of 12.27023581, we get
B = 4/D^2 + 1/(20-D)^2
B = 4/12.27023581^2 + 1/(20-12.27023581)^2
B = 4/12.27023581^2 + 1/7.72976419^2
B = 4/150.5586868 + 1/59.74925443
B = 0.026567713 + 0.016736611
B = 0.043304324
And the intuition value of 13.33333333
B = 4/D^2 + 1/(20-D)^2
B = 4/13.33333333^2 + 1/(20-13.33333333)^2
B = 4/13.33333333^2 + 1/6.666666667^2
B = 4/177.7777778 + 1/44.44444444
B = 0.0225 +0.0225
B = 0.045
And the calculated value is dimmer. So intuition wasn't correct.
So the object should be placed 4(4 - 2*2^(1/3) + 2^(2/3)) feet from the stronger light source, or approximately 12.27023581 feet.</span>
Answer:-
95 grams
Explanation:-
Let the mass of water to be added be M
So total mass = 5 + M
So 5% of this solution has 5g of NaCl by mass.
∴ (M+5) x (5/100) = 5
M+5 = 5 x 100/5
M+5=100
M= 100-5
95
So amount of water to be added is 95 gram
The pressure exerted by 0.400 moles of carbon dioxide in a 5.00 Liter container at 25 °C would be 1.9563 atm or 1486.788 mm Hg.
<h3>The ideal gas law</h3>
According to the ideal gas law, the product of the pressure and volume of a gas is a constant.
This can be mathematically expressed as:
pv = nRT
Where:
p = pressure of the gas
v = volume
n = number of moles
R = Rydberg constant (0.08206 L•atm•mol-1K)
T = temperature.
In this case:
p is what we are looking for.
v = 5.00 L
n = 0.400 moles
T = 25 + 273
= 298 K
Now, let's make p the subject of the formula of the equation.
p = nRT/v
= 0.400 x 0.08206 x 298/5
= 1.9563 atm
Recall that: 1 atm = 760 mm Hg
Thus:
1.9563 atm = 1.9563 x 760 mm Hg
= 1486.788 mm Hg
In other words, the pressure exerted by the gas in atm is 1.9563 atm and in mm HG is 1486.788 mm Hg.
More on the ideal gas law can be found here: brainly.com/question/28257995
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Answer:
Mass of hydrogen gas evolved is 0.0749 grams.
Explanation:
Total pressure of the gases = p = 758 mmHg
Vapor pressure of water = 23.78 mmHg
Pressure of hydrogen gas ,P = p - 23.78 mmHg = 758 mmHg - 23.78 mmHg
P = 734.22 mmHg = 
Temperature of of hydrogen gas ,T= 25°C =298.15 K
Volume of hydrogen gas = V = 0.949 L
Moles of hydrogen gas =n
PV = nRT (Ideal gas equation )
n = 0.03745 mol
Moles of hydrogen gas = 0.03745 mol
Mass of 0.03745 moles of hydrogen gas = 0.03745 mol × 2 g/mol = 0.0749 g
Mass of hydrogen gas evolved is 0.0749 grams.
Answer:
it would ether be gray to black or silver to gray and black
Explanation:
because of my calculation ekasillicon would be that color because of the eyes and because of your color seeing .
