PLEASE HELP WITH THIS IF I DONR GET IT RIGHT I WILL FAIL I WILL GIVE BRAINLIEST AND CORRECT ANSWE ONLY

Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3

Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

$\frac{dV}{dt} = -kA$

Using Euler's method

$\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i} \\$

Where initial droplet volume is:

$V(0) = \frac{4pi}{3} * r(0)^3 = \frac{4pi}{3} * 2.5^3 = 65.45 mm^3$

Hence, the iterative solution will be as next:

i = 1, ti = 0, Vi = 65.45

$V'_{i} = -k *4pi*(\frac{3*65.45}{4pi})^(2/3) = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88$

i = 2, ti = 0.5, Vi = 63.88

$V'_{i} = -k *4pi*(\frac{3*63.88}{4pi})^(2/3) = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33$

i = 3, ti = 1, Vi = 62.33

$V'_{i} = -k *4pi*(\frac{3*62.33}{4pi})^(2/3) = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813$

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

$r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\$

The average change of droplet radius with time is:

Δr/Δt = $\frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min$

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

5 0

3 years ago

What is the measurement of BC to the nearest centimeter?

77julia77 [94]

Answer:

a 8

Step-by-step explanation:

You are given two sides and the included angle. Since you don't have any side and the opposite angle, you must use the law of cosines.

$a^2 = b^2 + c^2 - 2bc\cos A$

$a^2 = 5^2 + 11^2 - 2(5)(11)\cos 39^\circ$

$a^2 = 25 + 121 - 110\cos 39^\circ$

$a^2 = 60.51$

$a = 7.779$

Answer: a = 8 cm

7 0

3 years ago

Please help me again one last time for this lol.

Darina [25.2K]

Answer:

3/8 = 9/24 ; 1/3 = 8/24 ; 3/8 > 1/3

Step-by-step explanation:

You have to multiply 8 and 3 to obtein the same number as denominatoe (24).

Once you have the same number you can use < = >

3 0

3 years ago

PLZ do this!!! I will give brainliest to anyone who does them all right. I need this done at 3:30 (it 2:44 right now)! No fake a

leva [86]

Answer:

A: y=1/3x+5

B: y=-2x+9

C: y=-3

D:y=2x+9

E: y=-10x+80

F:y=x-2

#1 rodney's error for

y=30x+10 is that he started off at 30 but he had to start off at 10 so it starts at (0,10) (1,40) (2,70) and keep going on by adding one to the x value and 30 to the y value

#2 rodneys error for

y=-1/2x+5 is that he went up by 1/2 instead of going down. it's a negative 1/2 so he had to go down

#3 Rodneys error for

y=x-2 is that he didn't start at (0.-2)

I'm not sure about the last picture but i think that it's

Tierra, Sharayah, Caleb, and Lang

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

How many times can four squares be put edge to edge

stepan [7]

four since it has four edges/sides

5 0

3 years ago