Answer:
a=6 and b=7
Step-by-step explanation:
Answer:
270 & 30
Step-by-step explanation:
let the number is n,
the equation :
n× 1/9 n= 27(n +1/9 n)
1/9 n² = 27n + 3n
1/9 n² = 30n
1/9n²- 30n = 0
n(1/9n -30)= 0
n = 0 or
1/9n = 30 => n = 30×9 = 270
270 is a number,
the other : 270/9 = 30
1
:x
2
+y
2
−6x−9y+13=0
(x−3)
2
+(y−
2
9
)
2
−9−
4
81
+13=0
(x−3)
2
+(y−
2
9
)
2
=
4
65
Here,
r
1
=
2
65
C
1
=(3,
2
9
)
Equation of another circle-
S
2
:x
2
+y
2
−2x−16y=0
(x−1)
2
+(y−8)
2
−1−64=0
(x−1)
2
+(y−8)
2
=65
Here,
r
2
=
65
C
2
=(1,8)
Distance between the centre of two circles-
C
1
C
2
=
(3−1)
2
+(8−
2
9
)
2
C
1
C
2
=
4+
4
49
=
2
65
∣r
2
−r
1
∣=
∣
∣
∣
∣
∣
∣
65
−
2
65
∣
∣
∣
∣
∣
∣
=
2
65
∵C
1
C
2
=∣r
1
−r
2
∣
Thus the two circles touches each other internally.
Since the circle touches each other internally. The point of contact P divides C
1
C
2
externally in the ratio r
1
:r
2
, i.e.,
2
65
:
65
=1:2
Therefore, coordinates of P are-
⎝
⎜
⎜
⎜
⎜
⎜
⎛
1−2
1(1)−2(3)
,
1−2
1(8)−2(
2
9
)
⎠
⎟
⎟
⎟
⎟
⎟
⎞
=(5,1)
Therefore,
Equation of common tangent is-
S
1
−S
2
=0
(5x+y−6(
2
x+5
)−9(
2
y+1
)+13)−(5x+y−2(
2
x+5
)−16(
2
y+1
))=0
2
−6x−9y−13
+x+8y+13=0
4x−7y−13=0
Hence the point of contact is (5,1) and the equation of common tangent is 4x−7y−13=0.
The answer is :
Y-21=-21/11 (X -7)
I only know how much does the fruit costs per pound is $4.82
