Option A
The solution is
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
3x + 6y = 1 ------ eqn 1
x - 4y = 1 ------ eqn 2
We have to find solution to system of equations
We can use substitution method
From eqn 2,
x = 1 + 4y -------- eqn 3
Substitute eqn 3 in eqn 1
3(1 + 4y) + 6y = 1
3 + 12y + 6y = 1
18y = 1 - 3
18y = -2
Divide both sides by 18
Substitute the above value of y in eqn 3
Thus solution is
Step-by-step explanation:
(i) Using the law of cosines, we can find that
≈ 0.62, so O ≈ 0.9
(ii) Since the whole pie has 2π radians (or 360 degrees), we can divide 0.9 by 2π to get around 6.9 slices from the pie
(iii) The area of the shaded segment can be found by finding sector OAB and subtracting triangle OAB from that. Sector OAB can be found by finding the area of the pie (π*8², since 8 is the radius) and dividing that by 6.9, so we get 64π/6.9 ≈ 29. Then, the area of the triangle is √p(p-a)(p-b)(p-c), with p being the perimeter and a, b, and c being the sides. Plugging 7, 8, and 8 in, we get 25.1781 as our area, so the difference is around 3.8