Give an example of a real-wrold situation in which the graphs of two equations in a linear system would be perpendicular. Describe the situation in words, write the equations, and show the graph. Explain how the solution to the system is related to the equations, the graph and the actual situation.
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2006-06-18 15:00:13 · 5 answers · asked by lisa_glenowicz 1 in Science & Mathematics ➔ Mathematics
Two airplanes are both travelling along linear courses, at fixed speeds. Both will pass over a specific place. At the same time, one plane is 500 miles east of the place; the other plane is 300 miles south of the place. If the east plane travels at 500 mph, what speed must the other plane travel at to collide with the first?
--keep in mind I've created a 3D system here--
Set the point of collision at the origin (0,0). Now we have:
x=500-500t
y=300-nt.
We're looking for n.
We know that t=t in order for them to collide.
Now solve for x=0 to find out when (the value of t) the first plane reaches the place of collision. t=1.
Place y=0 and t=1 to solve for n.
n=300mph.
You have to make your own graph.
2006-06-19 04:18:31 · answer #1 · answered by bequalming 5 · 0⤊ 0⤋
The most fundamental reason is to be able to solve polynomial equations. If you have an equation saying that a product of several factors must equal zero, the solution is that one or more of the factors must be zero. For example, suppose you throw a ball into the air and want to find when it hits the ground. Laws of physics tell you that the height of the ball t seconds after you threw it is a quadratic polynomial in t. Depending on how fast and at what angle you threw it, you might, for instance, discover from the laws of physics that the height of the ball is -4t^2+4t+5 . To find when it hits the ground, you want to find what value of t gives you -4t^2+4t+5 = 0 . A tough problem as it stands (until you learn about the quadratic formula). But if you're able to factor the left-hand side, you see that the equation is saying that (-t+5)(t+1)=0 and the only time this product is zero is when one of the factors is zero; in other words, when t=5 or t=-1. Ignoring the negative solution (because the ball didn't start moving until after you threw it), you see that the ball hits the ground five seconds after you threw it. You could explain to your students that they will learn a formula for solving any quadratic equation like this, but that factoring is the way such a formula comes about. Then you could also mention that knowing how a number factors tells you many useful things about it. For example, why is it that if you take any number and take the sum of that number, its cube, and three times its square, you always end up with a multiple of 6? The answer is because the polynomial (IMAGE) factors as (IMAGE) , and among any three consecutive numbers at least one must be even and at least one must be a multiple of 3, so the product is a multiple of 6.
2016-03-26 21:04:52 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Oh, how about the motion of a charged electric particle going in a circle in a plane and the magnetic field that it generates? Any diameter of the circle will have an equation that is perpendicular to the magnetic field generated.
2006-06-18 15:50:14 · answer #3 · answered by gandalf 4 · 0⤊ 0⤋
Maybe you could at least reword your homework question so it doesn't sound like a homework question or a take home quiz/test question.
2006-06-18 15:19:07 · answer #4 · answered by none2perdy 4 · 0⤊ 0⤋
maybe the great depression.. the stock markets were up then they went bankrupt....
2006-06-18 15:06:47 · answer #5 · answered by Anonymous · 0⤊ 0⤋