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jek_recluse [69]
3 years ago
8

The radius of a circular puddle is growing at a rate of 20 cm/sec. (a) how fast is its area growing at the instant when the radi

us is 40 centimeters? hint [see example 1.] (round your answer to the nearest integer.) incorrect: your answer is incorrect. cm2/s (b) how fast is the area growing at the instant when it equals 64 square centimeters? hint [use the area formula to determine the radius at that instant.] (round your answer to the nearest integer.)
Mathematics
1 answer:
Readme [11.4K]3 years ago
5 0
Part (a)
 
The expression for the circle area is given by:
 A = pi * r ^ 2
 Where,
 r: radio
 We now derive the expression of the area with respect to time:
 A '= 2 * pi * r * r'
 Substituting values:
 A '= 2 * pi * (40) * (20)
 A '= 5026.6 cm ^ 2 / s
 Answer:
 its area is growing at the instant when the radius is 40 centimeters at:
 A '= 5026.6 cm ^ 2 / s<span>
 Part b)
 A = pi * r ^ 2
 We look for the radio:
 r = root (A / pi)
 r = root (64 / pi)
 r = 4.5 cm
 We now derive the expression of the area with respect to time:
 A '= 2 * pi * r * r'
 Substituting values:
 A '= 2 * pi * (4.5) * (20)
 A '= 565.5 cm ^ 2 / s
 Answer:
 its area is growing at:
 A '= 565.5 cm ^ 2 / s</span>
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Yes, you are correct!
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A box with a square base and open top must have a volume of 32,000 cm3. find the dimensions of the box that mini- mize the amoun
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Alrighty


squaer base so length=width, nice


v=lwh
but in this case, l=w, so replace l with w
V=w²h

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the amount of materials is the surface area
note that there is no top
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L=W so
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SA=W²+4HW

alrighty

we gots
SA=W²+4HW and
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we want to minimize the square foottage
get rid of one of the variables
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subsitute

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take derivitive to find the minimum
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where does it equal 0?

0=2W-1280000/W²
128000/W²=2W
128000=2W³
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so sub back
32000/W²=H
32000/(40)²=H
32000/(1600)=H
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the box is 20cm height and the width and length are 40cm
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