You know that Akiko is 45 miles from the origin...Kosuke is (135/4) miles from the origin... You can draw a figure to clearly see the situation.
<span>you "know" that the angle between their routes is 140º </span>
<span>the side opposite (140º) is the distance between them... </span>
<span>c^2 = (45)^2 + (135/4)^2 - 2(45)(135/4) cos 140 </span>
<span>c ≈ 74.1 mile
Hope this answers the question.</span>
- Make an equation representing the number of vehicles needed.
We have six drivers so
x + y ≤ 6
That's not really an equation; it's an inequality. We want to use all our drivers so we can use the small vans, so
x + y = 6
- Make an equation representing the total number of seats in vehicles for the orchestra members.
s = 25x + 12y
That's how many seats total; it has to be at least 111 so again an inequality,
25x + 12y ≥ 111
We solve it like a system of equations.
x + y = 6
y = 6 - x
111 = 25x + 12y = 25x + 12(6-x)
111 = 25x + 72 - 12x
111 - 72 = 13 x
39 = 13 x
x = 3
Look at that, it worked out exactly. It didn't have to.
y = 6 - x = 3
Answer: 3 buses, 3 vans
Given:
The variable cost per unit is $3, fixed costs are $2.
The revenue function is:
where q is the number of thousands of units of output produced.
To find:
The break - even points for company X.
Solution:
The variable cost per unit is $3, fixed costs are $2.
So, the cost function is:
Total cost = Fixed cost + Variable cost × Quantity
The revenue function is:
At break - even points the profit is zero. It means the cost and revenue are equal.
Squaring both sides, we get
Splitting the middle term, we get
Using zero product property, we get
and 
and 
and
Therefore, the break even points are 0.444 and 1.
The function you're given is in point-slope format, which is one of the easiest ones to graph. The basic form of the format is;
y=ax+b
Where a is the slope and b is the y-intercept.
As you can see, in y=-13+3x, the positions of a and b are switched, but it is essentially the same question.
From here we can tell that the y-intercept is -13, meaning that there is a point on the line that rests at (0,-13)
To find the other points, we can do rise-over-run using the slope of 3 given to us. What happens here is that for every 1 unit you go to the right (positive), you rise 3 units up.
For example, if we perform this on the y-intercept (0,-13):
(0+1, -13+3)
(1,-10)
With these two points, you can graph the line representing the temperature.
