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jarptica [38.1K]
3 years ago
11

(b) What is 0.36 (six repeating) expressed as a fraction in simplest form?

Mathematics
1 answer:
zubka84 [21]3 years ago
3 0
 0.3666.....

If a number is repeating singly, just know it has to do with dividing by 9.

Let the number be x = 0.36....  (i)

Multiply both sides by 10.

10x = 3.66...         (ii)

Equation (ii) - (i)

10x - x = 3.66 - 0.36

9x = 3.3

x = 3.3/9

x = (33/10)*(1/9)

x = 33/90

x = 11/30

The simplest fraction is 11/30

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The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm.
Nat2105 [25]

Answer:

A) Maximum error = 170.32 cm³

B)Relative error = 0.0575

Step-by-step explanation:

A) Formula for circumference is: C = 2πr

Differentiating with respect to r, we have;

dC/dr = 2π

r is small, so we can write;

ΔC/Δr = 2π

So, Δr = ΔC/2π

We are told that ΔC = 0.5.

Thus; Δr = 0.5/2π = 0.25/π

Now, formula for Volume of a sphere is;

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Differentiating with respect to r, we have;

dV/dr = 4πr²

Again, r is small, so we can write;

ΔS/Δr = 4πr²

ΔV = 4πr² × Δr

Rewriting, we have;

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Since C = 2πr, we now have;

ΔV = (C²/π)Δr

ΔV will be maximum when Δr is maximum

Thus, ΔV = (C²/π) × 0.25/π

C = 82 cm

Thus;

ΔV = (82²/π) × 0.25/π

ΔV = 170.32 cm³

B) Formula for relative error = ΔV/V

Relative error = 170.32/((4/3)πr³)

Relative error = 170.32/((4/3)C³/8π³)

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3 0
2 years ago
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Answer:

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Let us revise the trigonometry functions

  • Sin(x) = opposite/hypotenuse
  • Cos(x) = adjacent/hypoteouse
  • Tan(x) = opposite/adjacent
  • Csc(x) = hypotenuse/opposit
  • Sec(x) = hypotenues/adjacent
  • Cot(x) = adjacent/opposite

In the given figure

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Hypotenuse = \sqrt{64+225}

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sinФ = 8/17

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sec Ф = 17/15

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