How many solutions 9x +2y =9 / -3x + y=2
1 answer:
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Step-by-step explanation:
Given : A rectangle 4 x 8 , a semicircle
Diagonal intersecting semicircle
To Find :Area of red part
<h3>Solution:</h3>Angle AC make AB α = ∠BAC
tan α = BC/AB = 4/8 = 1/2
=> α = 26.565°
∠ECA = ∠BAC = α
EC = EF = 4
=> ∠CEF = 180° - 2α
∠AED = 45° as AE is diagonal of Square of side 4
=> ∠AEF + 180° - 2α + 45° = 180°
=> ∠AEF = 2α - 45° = 8.13°
in Left side area between square and circle is split in 2 Equal parts
(1/2) area - area AFG = area of Red part
in Left side area between square and circle = 4² - (1/4)π4²
= 3.4336 sq unit
half = 1.7168 sq unit
Now find area AFG = area ΔAEF - sector EGF
area ΔAEF
AE = 4√2 , EF = 4 angle = 8.13°
area ΔAEF = (1/2) 4√2 * 4 sin 8.13° = 1.6 sq unit
area sector EGF = (8.13/360)π4² = 1.135 sq unit
area AFG = 1.6 - 1.135 = 0.465 sq unit
Area of Red part = 1.7168 - 0.465 sq unit
= 1.2518 sq unit
= 1.252 sq unit
= 1.25 sq unit.
Hope this helps!!
It takes about 14.55 years for quadruple your money
<em><u>Solution:</u></em>
Given that,
At 10 percent interest, how long does it take to quadruple your money
Rule of 144:
The Rule of 144 will tell you how long it will take an investment to quadruple
Here,
Rate of interest = 10 %
Therefore, number of years to quadruple your money is obtained by dividing 144 by 10
<em><u>Rule of 144 Formula: </u></em>
Where:
N = Number of many years times.
144 = Is the constant variable.
R = Rate of interest.
Thus it takes about 14.4 years for quadruple your money.
<em><u>Another method:</u></em>
If initial amount is $ 1 and it if quadruples it should be $ 4
We have to find the number of years if rate of interest is 10 %
Let "n" be the number of years
Then we can say,
Thus Option D 14.55 years is correct