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nata0808 [166]
3 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]3 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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Step-by-step explanation:

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One min after it ends
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Ubehebe Crater in Death Valley has a diameter of a little more
cupoosta [38]
First, we are going to use the formula of the circumference of a circle: C=2 \pi r
where 
C is the circumference of the circle.
r is the radius of the circle.

We know for our problem that the diameter of Ubehebe Crater is 1 mile. Since the radius of a circle is half its diameter, the radius of our crater will be: r= \frac{1}{2} =0.5. Lets replace that value in our formula:
C=2 \pi r
C=2*3.14*0.5
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Next, we are going to use the distance speed time formula: t= \frac{d}{s}
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4 0
3 years ago
What is the slope of the line 5(y+2) = 4(x-4)
Nadya [2.5K]

Answer: 4/5

Step-by-step explanation:

If you put the equation in point slope form, then the equation is...

y+2 = (4/5)(x-4)

Then we can identify the slope as 4/5.

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3 years ago
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PLEASEE help me ! :(
Mashutka [201]

HELLO EVERYONE,

TO FIND Y:

We know

a straight line makes an angle of 180

so,

180 = 119-y

180-119 = y

therefore y is

y = 59 degrees

TO FIND X:

We know,

all angles of a quadrilateral make a sum of 360,

so,

A+B+C+D = 360

HERE,

A = 131

B = 56

C = Y = 59

D = X

131 +56+59+X = 360

360 - 246 = X

X = 114 Degrees

Please do mark me the branliest if it helpful for you. Thanks.

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3 years ago
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