Step-by-step explanation:
<h3>#CMIIW</h3>
Answer:
- solution: (1/(1+m), m/(1+m))
- no solution for m = -1 (lines are parallel)
Step-by-step explanation:
Two distinct lines will always have a point of intersection, provided they are not parallel. That is, the system of equations {x +y = 1, y = mx} will have a unique solution as long as m ≠ -1.
The solution to the system can be found by substitution:
x +mx = 1
x(1 +m) = 1 . . . . factor out x
x = 1/(1+m) . . . . . divide by the coefficient of x; we must have m ≠ -1
y = m/(1+m) . . . . find the y-coordinate of the solution
The point of intersection is (1/(1+m), m/(1+m)).
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The above solution is undefined when the denominator is zero: m = -1. There is no solution for m = -1.
Answer:
1/10
Step-by-step explanation:
350/10 = 350 * X
35 = 350 * X
35/350 = X
X = 1/10
Let <em>a</em> denote the airplane's speed in still air, and <em>w</em> the windspeed.
When the plane flies against the wind, it can travel an average speed of
(4500 km) / (6 h) = 750 km/h
so that
<em>a</em> - <em>w</em> = 750 km/h
Flying with the wind, it moves at a speed of
(2910 km) / (3 h) = 970 km/h
so that
<em>a</em> + <em>w</em> = 970 km/h
Add the two equations to eliminate <em>w</em> and solve for <em>a</em> :
(<em>a</em> - <em>w</em>) + (<em>a</em> + <em>w</em>) = 750 km/h + 970 km/h
2<em>a</em> = 1720 km/h
<em>a</em> = 860 km/h
Subtract them to eliminate <em>a</em> and solve for <em>w</em> :
(<em>a</em> - <em>w</em>) - (<em>a</em> + <em>w</em>) = 750 km/h - 970 km/h
-2<em>w</em> = -220 km/h
<em>w</em> = 110 km/h
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