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Delvig [45]
3 years ago
5

Use differentials to approximate the change in the volume of a cube when the side is decreased from 8 to 7.99 cm. (in cm3)

Mathematics
1 answer:
Firlakuza [10]3 years ago
4 0

Answer:

  -1.92 cm³

Step-by-step explanation:

The formula for the volume of a cube in terms of side length is ...

   V = s³

Then the first-order approximation of volume for a small change ∆s in side length is ...

  V(s +∆s) ≈ V(s) + V'(s)·∆s

and the change in volume is ...

  ∆V ≈ V(s +∆s) -V(s) = V'(s)·∆s

The derivative V'(s) is ...

  V'(s) = 3s²

so the change in volume for s = 8 cm and ∆s = -0.01 cm is ...

  ∆V ≈ 3s²·∆s = 3(8 cm)²(-0.01 cm) = -1.92 cm³

 

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a = $80.3

b = $80

c = 4

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e = 4

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Step-by-step Explanation:

==>Increasing $72 by 10% to get a

a = 110% of $72 = 110% × $73

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a = $80.3

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b = 2^{c} * 5

Thus, 80 = 2⁴ * 5

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==>Calculating c² = d

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e = ²/8 × 16

e = 2 × 2

e = 4

==> e% of 2200 = f

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If £1 = $1.5,

£88 = $g

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==> i × (3 + 2) = j

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j = 6 × 5

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==> j% of 70 = k

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k = 30% × 70

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⅖ × $90 = m

m = 0.4 × 90

m = $36

==> √m + m = n

n = √36 + 36

n = 6 + 36

n = 42

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o = 21/50

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p = 21/50 × 250

p = (21 × 250)/50

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105 = 3 × 5 × 7

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Area = 56 cm²

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s = 8 × 0.3

s = 2.4

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t = 2.4 ÷ 0.6

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Since 1m = 100cm

4m = u cm

1 × u = 100 × 4

u = 400cm

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v = ⁷/10 × $400

v = 0.7 × 400

v = $280

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