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Sonja [21]
2 years ago
13

Part 4. NO LINKS!! Find the area of the shaded area shown. SHOW WORK PLEASE !! #21​

Mathematics
2 answers:
SIZIF [17.4K]2 years ago
5 0

Area of square

  • 32²
  • 1024

Radius of each circle

  • 32/4/2
  • 8/2
  • 4

Area of 16 circles

  • 16πr²
  • 16π(4)²
  • 16π(16)
  • 256π
  • 803.8cm²

Area of shaded region

  • 1024-803.8
  • 220.2cm²
Julli [10]2 years ago
3 0
<h2>Area of Shaded</h2>

Find the area of the shaded area shown.

<h3>Solution:</h3>

  • A = s²
  • A = 32cm
  • A = 32cm x 32cm
  • A = 1024
  • A = 32/4/2
  • A = 32 ÷ 2
  • A = 8
  • A = 8 ÷ 2
  • A = 4

So in the inscribed circle there are 16.

  • A = 16 radius ²
  • A = 16 x 4r²
  • A = 4 x 4
  • A = 16
  • A = 16π x 16
  • A = 256π
  • A = 256 x 3.14
  • A = 803.84
  • A = 1024cm - 803.84
  • A = 220.16cm²

#ProblemSolve

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19x^{r+1}y^{s+2}+7x^ry^s=rx^{r+1}y^{s+2}-rx^ry^s-7sx^{r+1}y^{s+2}-6sx^ry^s
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(7x^6y+6x^5y^{-1})\,\mathrm dx+(x^7-x^6y^{-2})\,\mathrm dy=0

Renaming M(x,y) and N(x,y) to our current coefficients, we end up with partial derivatives

M_y=7x^6-6x^5y^{-2}
N_x=7x^6-6x^5y^{-2}

as desired, so our new ODE is indeed exact.

Next, we're looking for a solution of the form \Psi(x,y)=C. By the chain rule, we have

\Psi_x=7x^6y+6x^5y^{-1}\implies\Psi=x^7y+x^6y^{-1}+f(y)

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\Psi_y=x^7-x^6y^{-2}=x^7-x^6y^{-2}+\dfrac{\mathrm df}{\mathrm dy}
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