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:
Each hiker carried the backpack for 1/5 of the total trail distance
Step-by-step explanation:
Three members of a teen hiking group hiked 3/5 of the entire Appalachian trail, each teen carried the backpack the same distance
=> each teen carried the backpack for = (1/3) (3/5) of total Distance = 1/5
3/4 *x-4
3/4 x 3/4 x 3/4 x 3/4
3 13/81
This question is not complete because is lacks the options for each question.
Complete question
mr. whittaker’s science class uses tide gauges to measure annual variations in water levels at different parts of a river, and then compares those variations to the average annual trend. matea recorded that the water level in one part of the river fell 1.05 millimeters per year for 2.48 years. this data will be compared to the average annual trend, which shows the water level rising 1.8 mm/year.
1) Which number represents the rate at which the water level fell?
a. -1.05 mm/year
b. -1.8 mm/year
c. -2.48 years
d. -2.48 mm/year
2) Which number should the rate be multiplied by to find the total variation in water level?
a. 1.05 mm/year
b. 1.8 mm/year
c. 2.48 years
d. 2.48 mm/year
Answer:
1) Which number represents the rate at which the water level fell?
a. -1.05 mm/year
2) Which number should the rate be multiplied by to find the total variation in water level?
c. 2.48 years
Step-by-step explanation:
Total Variation in the water level is calculated by multiplying the rate at which the water level and number or years at which the rate of the water level fell
From the question, we can see that the rate at which the water level fell is -1.05 mm/year and number of years at which the water level fell is 2.48mm
Hence,Total Variation in the water level is calculated as
-1.05 mm/year × 2.48 years
Total variation in the water level = -2.604mm
3 km = 3000m
600m:3000m divide by 10
60:300 divide by 10
6:30 divide by 3
2:10 divide 2
*1:5* (simplest form)
