3. Simplify: 10√6 – 2√216 + 196
Answers
Step-by-step explanation:
One of the laws of indices states:
q
√
x
p
=
x
p
q
So,
(
216
1000
)
2
3
means the same as
3
√
216
1000
2
Note that
216
and
1000
are both perfect cubes.
216
=
6
3
and
1000
=
10
3
3
√
(
216
1000
)
2
←
find the cube roots first
=
(
6
10
)
2
←
simplify the fraction
=
(
3
5
)
2
←
square the fraction
=9/25
Answer:
Area of a circular disc is given by the formula, A = πr^2, where r=radius of the circular disc.
This area of πr^2 is for 360° central angle.
Therefore, area of the sector of the circular disc having central angle 1° is (πr^2)/360.
Then, area of the sector with x° central angle = (Area of the sector having central angle 1°) × x.
= x × {(πr^2)/360}.
Now put 120, 150, and 90 in the place of x in the above equation ( for the three sectors mentioned in the given question ).
We get the areas as 120 × {(πr^2)/360}, 150 × {(πr^2)/360}, and 90 × {(πr^2)/360} respectively.
Then, the ratio of the area of the above-mentioned three sectors is 120×{(πr^2)/360} : 150×{(πr^2)/360} : {(90×{(πr^2)/360)}.
Since “ {(πr^2)/360} ”is present in all the three terms of the ratio, it can be eliminated on division of the members by that value and the ratio becomes 120 : 150 : 90.
Then, we can simplify 120 : 150 : 90 as (3×4×10) : (3×5×10) : (3×3×10).
Let us eliminate” 3×10 ”from them, the ratio finally becomes 4 : 5 : 3 (ANS).
Method (2):
Let “A” be the area of the given circular disc.
Then, area of each sector with central angles 120°, 150°, and 90° will be A× 120 ÷ 360, A× 150 ÷ 360, and A× 90 ÷ 360, respectively.
Therefore, their ratio is, 120A/360 : 150A/360 : 90A/360.
Dividing all by 30A/360, we get the ratio 4 : 5 : 3 (ANS)