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stepladder [879]
3 years ago
13

Suppose a cup of coï¬ee is at 100 degrees Celsius at time t = 0, it is at 70 degrees at t = 10 minutes, and it is at 50 degrees

at t = 20 minutes. Compute the ambient temperature.
Physics
1 answer:
Alexandra [31]3 years ago
6 0

Answer:

T ambient = 10 degrees

Explanation:

Using Newton's Law of Cooling:

T(t) = Tamb + (Ti - Tamb)*e^(-kt)  ..... Eq 1

Ti = 100

We have two points to evaluate the above equation as follows:

T = 70 @ t = 10 using Eq 1  

70 = Tamb + (100 - Tamb)*e^(-10k)   ... Eq 2

T = 50 @ t = 20 using Eq 1

50 = Tamb + (100 - Tamb)*e^(-20k)   ... Eq 3

Solving the above Eq 2 and Eq 3 simultaneously:

Using Eq 2:

(70 - Tamb) / (100 - Tamb) = e^(-10k)  

Squaring both sides we get:

((70 - Tamb) / (100 - Tamb))^2 = e^(-20k)   .... Eq 4

Substitute Eq 4 into Eq 3

50 = Tamb + (100 - Tamb)*((70 - Tamb) / (100 - Tamb))^2

After simplification:

50 = (Tamb (100-Tamb) + (70-Tamb)^2) / (100 - Tamb)

5000 - 50*Tamb = 4900 - 40*Tamb

Tamb = 100 / 10 = 10 degrees

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Solution :

Michaelis-Menten kinetics in the field of biochemistry is considered as one of the well known models for enzyme kinetics. The model represents an equation that describes the enzymatic reactions's rate by relating the reaction rate to the substrate's concentration. The equation is named after the two famous scientists,  Leonor Michaelis and Maud Menten.

The formula is :

$v=\frac{V_{max}[S]}{K_M + [S]}$

where v = velocity of reaction

           $V_{max}$ = maximum rate achieved

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           [S] = concentration of the substrate, S

According to the question, by putting the velocity of reaction, v as $\frac{V_{max}}{4}$, we get the above equation as

$[S]= \frac{K_M}{3}$

Therefore the answer is $[S]= \frac{K_M}{3}$

3 0
2 years ago
Los resortes tienen masa, ¿El periodo y la frecuencia reales son mayores que los dados en las ecuaciones para una masa oscilante
MrRa [10]

Answer:

me no speek spanish

Explanation:

4 0
3 years ago
1)Light of wavelength 588.0 nm is incident on a narrow slit. The diffraction pattern is viewed on a screen 55.5 cm from the slit
Talja [164]

Answer:

These are Diffraction Grating Questions.

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Given as  

y = nDλ/w                                                       Eqn 1

where  

w = width of slit  

D = distance to screen  

λ = wavelength of light  

n = order number  

Making x the subject of the formula gives,  

w = nDλ/y  

Given  

y = 0.0149 m  

D = 0.555 m  

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w = 6.6x10⁻⁵m

Hence, the width of the slit w, in micrometers (μm) = 66μm

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w = 0.1mm = 1.0x10⁻⁴m

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y₉ = 9 x 0.27 x 632 x 10-9/ 1.0x10⁻⁴m = 0.015m

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y₅ = 5x 0.27 x 632 x 10-9/ 1.0x10⁻⁴m = 0.0085m

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8 0
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Why is it that the weight of an object weighing 1N air, weighs more when immersed in water ?
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The object is lifted by a force equal to the weight of the fluid it displaces.
It displaces the same amount of air or water, and any amount of water
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4 0
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Answer:

Explanation:

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