The rate of the current is 6 mile/hour.
<h3>
What does a rate mean ?</h3>
In this context, the rate is tantamount to speed o velocity in a linear motion. The S.I unit will be mile per hour.
Given that a boat takes 10 hours to sail a distance of 100 nautical miles with the current. The rate at which the boat move will be
The rate R1 = 100/10
R1 = 10 mile/hour
And when it moves against the current, it takes the boat 25 hours to sail the same distance. The rate at which the boat move will be
The rate R2 = 100/25
R2 = 4 mile/hour
The rate of the current R will be the difference between the two calculated rate. That is,
R = R1 - R2
R = 10 - 4
R = 6 mile/hour
Therefore, the rate of the current is 6 mile/hour.
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This is the net of a rectangular prism, so the surface area can be found with the formula: SA=2lw+2wh+2lh
In this case,
l=10.5
w=6.4
h=4
Now, we can plug these numbers into the equation:
SA= (2)(10.5)(6.4) + (2)(6.4)(4) + (2)(10.5)(4)
SA= 134.4 + 51.2 + 84
SA = 269.6 cm
Therefore, the answer is D.
Answer:
<h2>Required set will be :-</h2><h3>(9,15)</h3>
1. M is the midpoint of LN and O is the midpoint of NP. This makes the triangle MNO equal to half of LNP. Then you can get this equation
MO= (1/2) LP
If you insert MO = 2x +6 and LP = 8x – 20 the calculation would be:
2x+6= (1/2)( 8x-20)
2x+6= 4x-10
2x-4x= -10 - 6
-2x= -16
x=8
2. Centroid is the point that intersects with three median lines of the triangle. The centroid should divide the median lines into 1:2 ratio. In AC lines, A located in the base so A.F:FC would be 1:2
Then, the answer would be:
A.F= 1/(1+2) * AC
A.F= 1/3 * 12= 4
FC= 2/(1+2) * AC
FC= 2/3 * 12= 8
3. Since
∠BAD=∠DAC
∠ABD=∠ACD
AD=AD
The triangle ABD and ACD are similar. You can get this equation
BD=DC
x+8= 3x+12
x-3x= 12-8
-2x=4
x=-2
DC=3x+12= 3(-2) +12= 6
4. Orthocenter made by intersection of triangle altitude
A
BC lines slope would be (-4)-(-1)/1-4= -3/-3= 1. The altitude line slope would be -1, the function would be:
y=-x +a
0= 1+a
a=-1
y=-x-1
B
AC lines slope would be (-4)-(-1)/1-0= -3. The altitude line slope would be 1/3, the function would be:
y=1/3x+a
-1=1/3(4)+a
a=-7/3
y=1/3x - 7/3
C
BC lines slope would be (-1)-(-1)/4 = 0/4.
The line would be
0=x+a
a=-1
0=x-1
x=1
y=-x-1 = 1/3x-7/3
-x-(1/3x)=-7/3 +1
-4/3x= -4/3
x=1
y=-x-1
y=-1-1= -2
The orthocenter would be (1,-2)
5.
a. Circumcenter: the intersection of perpendicular bisector lines<span>
b. Incenter: the intersection of bisector lines
c. Centroid: </span>the intersection of median lines<span>
d. Orthocenter: </span>the intersection of altitude lines
The answer is A
Hope that helps
