What is the value of NICO ? 81 16 16 81 16 81 81 16

Let $DEF$ be an equilateral triangle with side length $3.$ At random, a point $G$ is chosen inside the triangle. Compute the pro

umka21 [38]

$|\Omega|=(\text{the area of the triangle})=\dfrac{a^2\sqrt3}{4}=\dfrac{3^2\sqrt3}{4}=\dfrac{9\sqrt3}{4}\\|A|=(\text{the area of the sector})=\dfrac{\alpha\pi r^2}{360}=\dfrac{60\pi \cdot 1^2}{360}=\dfrac{\pi}{6}\\\\\\P(A)=\dfrac{\dfrac{\pi}{6}}{\dfrac{9\sqrt3}{4}}\\\\P(A)=\dfrac{\pi}{6}\cdot\dfrac{4}{9\sqrt3}\\\\P(A)=\dfrac{2\pi}{27\sqrt3}\\\\P(A)=\dfrac{2\pi\sqrt3}{27\cdot3}\\\\P(A)=\dfrac{2\pi\sqrt3}{81}\approx13.4\%$

8 0

3 years ago

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If triangle ABC defined by the coordinates A(1,1), B(9,1), C(1,9) is dilated by a scale factor of 1/2

alukav5142 [94]

Answer:

The transformed points of the triangle ABC are $A' (x,y) = \left( \frac{1}{2}, \frac{1}{2}\right)$ , $B'(x,y) = \left(\frac{9}{2}, \frac{1}{2} \right)$ , $C'(x,y) = \left(\frac{1}{2}, \frac{9}{2}\right)$

Step-by-step explanation:

The new points after applying the scale factor are, respectively:

$A' (x,y) = \frac{1}{2}\cdot (1,1)$

$A' (x,y) = \left( \frac{1}{2}, \frac{1}{2}\right)$

$B' (x,y) = \frac{1}{2}\cdot (9,1)$

$B'(x,y) = \left(\frac{9}{2}, \frac{1}{2} \right)$

$C'(x,y) = \frac{1}{2}\cdot (1,9)$

$C'(x,y) = \left(\frac{1}{2}, \frac{9}{2}\right)$

7 0

3 years ago

Sean bought 68 3/4 inches of rope . How many 15-inches ropes can he make from it

choli [55]

Length of rope bought by Sean = 68 3/4 inches
 = 275/4 inches
Then
The number of 15 inch rope that can be made by Sean = (275/4)/15
 = 275/(4 * 15)
 = 275/60
 = 4.58
So we can see from the above deduction that Sean can make 4 complete 15 inches ropes and there will be 0.58 inches of rope excess. I hope the procedure and the method of solving is absolutely clear to you. This is the easiest way to get to the solution for such problems.

6 0

3 years ago

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Which numbers belong to the solution of the equation x+10=14

Tatiana [17]

Answer:

The solution to this equation is x = 4

Step-by-step explanation:

To find this start with the original equation and subtract 10 from each side.

x + 10 = 14

x = 4

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