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4 years ago

The circle above has a radius of 8 cm. What is the area of the circle?

Mathematics

1 answer:

Naddik [55]4 years ago

7 0

Area of the circle is 200.96 cm²

Step-by-step explanation:

Step 1: Calculate area of the circle using the formula, A = π × r². Here r = 8cm.

⇒ Area = 3.14 × 8 × 8 = 200.96 cm²

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The sum of 2 fractions is 5/6. Their difference is 1/2. Their least common denominator is 6. The denominator of one is twice the

valentinak56 [21]

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the first fraction is : $\frac{a}{b}$

Suppose the second fraction is : $\frac{c}{d}$

The sum of both fraction is given as : $\frac{5}{6}$

$\frac{a}{b}+\frac{c}{d}=\frac{5}{6}$ .......................equation (1)

The difference of both fraction is given as : $\frac{1}{2}$

$\frac{a}{b}-\frac{c}{d}=\frac{1}{2}$ .........................equation (2)

Adding equation (1) and equation (2)

$\frac{c}{d} \ will \ be \ cancelled$

$\frac{2a}{b}=\frac{5}{6}+\frac{1}{2}$

making common denominator

$\frac{2a}{b}=\frac{5}{6}+ \frac{3}{6}$

$\frac{2a}{b}=\frac{8}{6}$

Hence,

$\frac{a}{b}=\frac{2}{3}$

Plugging the value of $\frac{a}{b}$ in equation (1)

$\frac{2}{3}+\frac{c}{d}=\frac{5}{6}$

Subtracting $\frac{2}{3}$ in both sides

$\frac{c}{d}=\frac{5}{6}-\frac{2}{3}$

$\frac{c}{d}=\frac{1}{6}$

Hence both fractions are $\frac{2}{3} \ and \ \frac{1}{6}$ ...................Answer

Hope it will help :)

7 0

3 years ago

Suppose F⃗ (x,y)=4yi⃗ +2xyj⃗ . Use Green's Theorem to calculate the circulation of F⃗ around the perimeter of a circle C of radi

Juliette [100K]

Answer:

-9π

Step-by-step explanation:

∫c (4y dx + 2xy dy)

= ∫∫ [(∂/∂x)(2xy) - (∂/∂y)(4y)] dA, by Green's Theorem

= ∫∫ (2y - 4) dA

Now convert to polar coordinates:

∫(r = 0 to 3) ∫(θ = 0 to 2π) (2r sin θ - 4) * (r dθ dr) --- first integration

= ∫(r = 0 to 3) (-2r cos θ - 4θ) * r {for θ = 0 to 2π} dr

= ∫(r = 0 to 3) -2πr dr

= -πr² {for r = 0 to 3}

= -π(3²) - -π(0)²

= -9π

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Answer:

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Step-by-step explanation:

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