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nata0808 [166]
2 years ago
9

Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportiona

l to its surface area. Show that under these circumstances the drop's radius increases at a constant rate.
Mathematics
1 answer:
NeX [460]2 years ago
6 0
The volume of a sphere is given by

V= \frac{4}{3} \pi r^3

The area of a sphere is given by

A=4\pi r^2

\frac{dV}{dt} \propto A \\  \\ \frac{dV}{dt} = kA

But

\frac{dV}{dt} =4\pi r^2 \frac{dr}{dt}

By substitution,

4\pi r^2 \frac{dr}{dt}=kA \\  \\ \Rightarrow4\pi r^2 \frac{dr}{dt}=4k\pi r^2 \\  \\  \frac{dr}{dt} =k

Thus, the <span>drop's radius increases at a constant rate.</span>
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Three consecutive integers whose sum is -147
suter [353]

Step-by-step explanation:

Let the first integer be x

2nd integer = x + 1

3rd integer = x + 2

x + x + 1 + x + 2 = -147

3x + 3 = -147

3x = -147 - 3

3x = -150

x = -150 ÷ 3

x = -50

The three consecutive integers are

-50, -49, -48

5 0
3 years ago
A square has a perimeter of 52cm , what is the area ?
UNO [17]

✧・゚: *✧・゚:*    *:・゚✧*:・゚✧

                  Hello!

✧・゚: *✧・゚:*    *:・゚✧*:・゚✧

❖ The area is 169 square cm.

Find the value of each side (a square has 4 sides so divide by 4 ):

52/4 = 13

To find the area of a square, you only need 2 sides so multiply 2 sides:

13 x 13 = 139

Area = 139 square cm

~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡

~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ

4 0
2 years ago
What do you call the second degre function?
Marina CMI [18]

Answer:

i think is Quadratic function

3 0
2 years ago
Read 2 more answers
Como seria una ecuacion de (2,3) si la pendiente es -2​
xxTIMURxx [149]

Answer:

Hola, antes de dar la respuesta quisiera recomendarte una app llamada m a t h w a y (sin espacios) esto te va a ayudar con preguntas sobre matematica y super rapido.

Step-by-step explanation:

(2,3) pendiente de -2

                                           1. Usa la fórmula de la ecuación de la recta para

                                              hallar b

y = mx + b

                                          2.  Substituye el valor de m, x y "y" en la ecuacion

3 = (-2) · (2) +b                      

                                           3. Calcula para hallar el valor de b

b = 7

                                          4. Ahora con el valor de b, calcule de nuevo

y = mx + b

3 = -2x +7

Espero esto haya ayudado en algo, sino puedes intentar buscando en el sitio que recomende.      

3 0
2 years ago
Given that f(x) = x2 + 12x + 32 and g(x) = 2 + 4, find (f - g)(x) and
Snowcat [4.5K]

Answer:

(f - g)(x) = x² + 12x + 26

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Distributive Property

<u>Algebra I</u>

  • Terms/Coefficients/Degrees

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = x² + 12x + 32

g(x) = 2 + 4

(f - g)(x) is f(x) - g(x)

<u>Step 2: Find</u>

  1. Substitute:                         (f - g)(x) = x² + 12x + 32 - (2 + 4)
  2. Combine like terms:         (f - g)(x) = x² + 12x + 32 - 6
  3. Combine like terms:         (f - g)(x) = x² + 12x + 26
7 0
2 years ago
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