Find the exact value of the area of a circle whose radius is 3.1

Mathematics

2 answers:

Kazeer [188]2 years ago

7 0

Answer:

Area = pi r²

Area = 22/7 × 3.1 × 3.1 = 30.202 unit²

GuDViN [60]2 years ago

4 0

Step-by-step explanation:

$area \: of \: circle = \pi \: {r}^{2} \\ = 3.14 \times {(3.1)}^{2} \\ = 3.14 \times 9.61 \\ = 30.1754 \: {unit}^{2} \\$

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Solve for x, 0 ≤ x ≤2π (2cosx-1)(2sinx+√3 ) = 0

vladimir1956 [14]

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x = π/3, x = 5π/3, x = 4π/3

Step-by-step explanation:

Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.

$2\cos \left(x\right)-1=0,\\2\cos \left(x\right)=1,\\\cos \left(x\right)=\frac{1}{2}$

Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.

Similarly:

$\:2\sin \left(x\right)+\sqrt{3}=0,\\2\sin \left(x\right)=-\sqrt{3},\\\sin \left(x\right)=-\frac{\sqrt{3}}{2}$