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PolarNik [594]
3 years ago
10

A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at

a rate of 0.5 m2/sec at what rate is the radius decreasing when the area of the sheet is 12 m2

Mathematics
2 answers:
elena-14-01-66 [18.8K]3 years ago
7 0

Answer:

dx/dt  =  0,04 m/sec

Step-by-step explanation:

Area of the circle is:

A(c) =π*x²      where   x is a radius of the circle

Applying differentiation in relation to time we get:

dA(c)/dt   =  π*2*x* dx/dt    

In this equation we know:

dA(c)/dt  = 0,5 m²/sec

And are looking for dx/dt then

0,5  = 2*π*x*dx/dt    when the area of the sheet is 12 m²  (1)

When  A(c) = 12 m²      x = ??

A(c)  =  12  =  π*x²      ⇒    12  =  3.14* x²    ⇒  12/3.14  =  x²

x²  = 3,82     ⇒   x  = √3,82    ⇒  x = 1,954 m

Finally plugging ths value in equation (1)

0,5  = 6,28*1,954*dx/dt

dx/dt  =  0,5 /12.28

dx/dt  =  0,04 m/sec

bezimeni [28]3 years ago
6 0

Answer:

dr/dt= 0.04m/s

Step-by-step explanation:

The steps are shown in the file attached

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Answer:

Step-by-step explanation:

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3 0
3 years ago
Which system of inequalities is represented by the graph?
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The blue line...
(1,2),(3,1)
slope = (1 - 2) / (3 - 1) = -1/2
there is a y int at (0,2.5) or (0,5/2)
it is shaded below the line....and it is a solid line
this inequality is :
y = -1/2x + 5/2
1/2x + y = 5/2
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red line...
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there is a y int at (0,4)
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summary :
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3 years ago
The measure of each interior angle of a regular polygon is 150 how many sides does the polygon have?
Dmitry [639]
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Step-by-step explanation:

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Vlad1618 [11]

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The ratio of the length and the breadth of rectangle=2:1

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