The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)
4x+3y=12
3y=-4x+12
y=-4x/3+12/3
So a line perpendicular to the bank will be:
y=3x/4+b, and we need it to pass through (7,5) so
5=3(7)/4+b
5=21/4+b
20/4-21/4=b
-1/4=b so the perpendicular line is:
y=3x/4-1/4
So now we want to know the point where this perpendicular line meets with the river bank. When it does y=y so we can say:
(3x-1)/4=(-4x+12)/3 cross multiply
3(3x-1)=4(-4x+12)
9x-3=-16x+48
25x=51
x=51/25
x=2.04
y=(3x-1)/4
y=(3*2.04-1)/4
y=1.28
So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(7-2.04)^2+(5-1.28)^2
d^2=38.44
d=√38.44
d=6.2 units
Since he can run at 10 uph...
t=d/v
t=6.2/10
t=0.62 hours (37 min 12 sec)
So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.
Answer:
x = 5, y = -2
Step-by-step explanation:
<u>Given equations:</u>
<u>From the first equation we get:</u>
<u>Substitute x in the second equation, find y:</u>
- 3x - y = 17
- 3*(1-2y) - y = 17
- 3 - 6y - y = 17
- -7y = 17 - 3
- -7y = 14
- y = -14/7
- y = -2
<u>Find x:</u>
- x = 1 - 2y
- x = 1 - 2*(-2)
- x = 1 + 4
- x = 5
Answer:
the answer is 8x^3
Step-by-step explanation:
because thats the answer
The oldest son will get $370, the middle will get $220 and the youngest will get $185.
Step-by-step explanation:
Given,
Total amount to be split = $775
Let,
Oldest son's share = x
Middle son's share = y
Youngest son's share = z
According to given statement;
x+y+z=775 Eqn 1
the oldest gets twice as much as the youngest
x = 2z Eqn 2
the middle son gets $35 more than the youngest
y = z+35 Eqn 3
Putting value of x and y from Eqn 2 and 3 in Eqn 1
Dividing both sides by 4
Putting z=185 in Eqn 2
Putting z=185 in Eqn 3
The oldest son will get $370, the middle will get $220 and the youngest will get $185.
Keywords: linear equation, substitution method
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