Answer:
16
Step-by-step explanation:
12+4=16
461.176470588
Explanation:
2×56=112
112×420=47040
---------------------------------
3×34=102
---------------------------------
47040÷102=461.176470588
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.
Answer:
69.94 miles
Step-by-step explanation:
The distance d₁ the first ship moves after 3 hours is 3 hours × 15 miles per hours = 45 miles
The distance d₂ the second ship moves after 3 hours is 3 hours × 12 miles per hours = 36 miles.
The angle the first ship's direction makes in the North-East direction is 90° - 75° = 15°
The angle the second ship's direction makes in the South-West direction = 14°
The distance moved by the two ships form the side of a triangle. The angle, θ between the two ship directions is 14° + 90° + 15° = 119°
Using the cosine rule, we find the distance d between the two ships
d = √(d₁² + d₂² -2d₁d₂cosθ)
= √(45² + 36² -2×45×36cos119°)
= √(2025 + 1296- (-1570.78))
= √(3321 + 1570.78)
= √4891.78
= 69.94 miles
Answer:
uh no new copy
Step-by-steYou can make a new table to add the amounts and copy the pre-existing amounts or just add a new bar, but I guess it will be better if you just do it again.
