Add Math( Part 3)
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Part 3 Area of flower plot = y m2
a.
y = (25/2) π - (1/2(x/2)2 π + 1/2((10-x )/2)2 π) = (25/2) π - (1/2(x/2)2 π + 1/2((100-20x+x2)/4) π) = (25/2) π - (x2/8 π + ((100 - 20x + x2)/8) π) = (25/2) π - (x2π + 100π – 20x π + x2π )/8 = (25/2) π - ( 2x2– 20x + 100)/8) π =
(25/2) π - (( x2 – 10x + 50)/4)
=
(25/2 - (x2 - 10x + 50)/4) π
y=
b.
((10x – x2)/4) π
y = 16.5 m2 16.5 = 66 =
((10x – x2)/4) π (10x - x2) 22/7
66(7/22) = 10x – x2 0 = x2 - 10x + 21 0 = (x-7)(x – 3) x=7 , x=3
c.
y=
((10x – x2)/4) π
y/x = (10/4 - x/4) π
x 1 y/x 7.1
2 6.3
When x = 4.5 , y/x = 4.3 Area of flower plot = y/x * x = 4.3 * 4.5 = 19.35m2
3 5.5
4 4.7
5 3.9
6 3.1
7 2.4
d. Differentiation method dy/dx = ((10x-x2)/4) π = ( 10/4 – 2x/4) π 0 = 5/2 π – x/2 π 5/2 π = x/2 π x = 5
Completing square method y=
((10x – x2)/4) π
=
5/2 π - x2/4 π
=
-1/4 π (x2 – 10x)
y+ 52 = -1/4 π (x – 5)2 y = -1/4 π (x - 5)2 - 25 x–5=0 x=5
Tn (flower
Diameter
bed)
(cm)
e.
T1 T2 T3 T4 T5 T6
30 39.697 49.394 59.091 68.788 78.485
T7 T8 T9 T10 T11 T12
88.182 97.879 107.576 117.273 126.97 136.667
n = 12, a = 30cm, S12 = 1000cm
S12 = n/2 (2a + (n – 1)d 1000 = 12/2 ( 2(30) + (12 – 1)d) 1000 = 6 ( 60 + 11d) 1000 = 360 + 66d 1000 – 360 = 66d 640 = 66d d = 9.697
a.
y = (25/2) π - (1/2(x/2)2 π + 1/2((10-x )/2)2 π) = (25/2) π - (1/2(x/2)2 π + 1/2((100-20x+x2)/4) π) = (25/2) π - (x2/8 π + ((100 - 20x + x2)/8) π) = (25/2) π - (x2π + 100π – 20x π + x2π )/8 = (25/2) π - ( 2x2– 20x + 100)/8) π =
(25/2) π - (( x2 – 10x + 50)/4)
=
(25/2 - (x2 - 10x + 50)/4) π
y=
b.
((10x – x2)/4) π
y = 16.5 m2 16.5 = 66 =
((10x – x2)/4) π (10x - x2) 22/7
66(7/22) = 10x – x2 0 = x2 - 10x + 21 0 = (x-7)(x – 3) x=7 , x=3
c.
y=
((10x – x2)/4) π
y/x = (10/4 - x/4) π
x 1 y/x 7.1
2 6.3
When x = 4.5 , y/x = 4.3 Area of flower plot = y/x * x = 4.3 * 4.5 = 19.35m2
3 5.5
4 4.7
5 3.9
6 3.1
7 2.4
d. Differentiation method dy/dx = ((10x-x2)/4) π = ( 10/4 – 2x/4) π 0 = 5/2 π – x/2 π 5/2 π = x/2 π x = 5
Completing square method y=
((10x – x2)/4) π
=
5/2 π - x2/4 π
=
-1/4 π (x2 – 10x)
y+ 52 = -1/4 π (x – 5)2 y = -1/4 π (x - 5)2 - 25 x–5=0 x=5
Tn (flower
Diameter
bed)
(cm)
e.
T1 T2 T3 T4 T5 T6
30 39.697 49.394 59.091 68.788 78.485
T7 T8 T9 T10 T11 T12
88.182 97.879 107.576 117.273 126.97 136.667
n = 12, a = 30cm, S12 = 1000cm
S12 = n/2 (2a + (n – 1)d 1000 = 12/2 ( 2(30) + (12 – 1)d) 1000 = 6 ( 60 + 11d) 1000 = 360 + 66d 1000 – 360 = 66d 640 = 66d d = 9.697
