Question

Math help pls

Answer 1

@Hero

Answer 2

In order to be able to do this you have to be familiar with Pythagorean Theorem and Systems of Equations. But you're probably just wondering how to even start.

Answer 3

What you want to do is start by splitting the highway into two lengths: \(y\) and \(500 - y\)

Answer 4

From here you apply the pythagorean theorem to the two smaller right triangles to get
\(x^2 + y^2 = 300^2\) and \(x^2 + (500 - y)^2 = 400^2\)

Answer 5

We only need to find \(x\)

Answer 6

We can eliminate the y's

Answer 7

ok, you gave 2 equations: x^2+y^2=300^2, and then x^2-(500-y)^2=400^2, which one am I supposed to solve?

Answer 8

You solve both .... SIMULTANEOUSLY (If you've ever heard of that)

Answer 9

confession: I have no idea wth you're saying
in order to solve this I'd need to have an x and y, right? what are those?

Answer 10

They are unknown variables. Solving two equations simultaneously is just a fancy way of saying you have to use a system of equations to find the values of x and y.

Answer 11

But before we create the system, we first have to expand \((500 - y)^2\)

Answer 12

Actually, I take that back. We'll have to eliminate the x's then solve for y before we can solve for x.

Answer 13

Sorry, you have to subtract the equation of the smaller triangle from the equation of the bigger triangle.

Answer 14

After subtracting you get

Answer 15

400^2-300^2=70000

Answer 16

I don't know if you used a calculator to get that but what I always do is use difference of squares to calculate that. \((400 + 300)(400 - 300)\) = \((700)(100) = 70000\)

Answer 17

so, what do I do now? (and yes, I used a calculator)

Answer 18

NOW, you can expand \((500 - y)^2\)

Answer 19

using what? what is y?

Answer 20

Y is the distance from Blare to the Service station along the highway.

Answer 21

Once we find \(y\) we can easily find \(x\)

Answer 22

how do we find y?

Answer 23

As I said before, the next step is to expand \((500 - y)^2\)

Answer 24

isn't y supposed to be a number?

Answer 25

It's an unknown variable until we solve for it.

Answer 26

(500-y(what am I supposed to subtract?))^2

Answer 27

The 500 - y is squared, meaning you have to do binomial expansion. Remember:
\((a - b)^2 = (a - b)(a - b)\)

Answer 28

and \((a - b)(a - b) = a^2 - 2ab + b^2\)

Answer 29

500^2=250000

Answer 30

so, 250000-500-y?

Answer 31

Not quite

Answer 32

250000-2(500-y) + y^2?

Answer 33

How do you figure?

Answer 34

500/300=400/x

Answer 35

Yeah, that's the other way to do it. @dude must have helped you.

Answer 36

which means 3*400/5= 240
no, ( I searched online, found a similar problem, applied it to this)

Answer 37

You were that desperate I suppose.

Answer 38

yes, I seriously was

Answer 39

Good on you

Answer 40

why are you always so bitter?

Answer 41

How does "Good on you" translate to "I'm bitter?".

Answer 42

"you were that desperate, I suppose" , you sound like a 90-year old bachelor whose just annoyed all the time

Answer 43

I have grandparents like that

Answer 44

I'll withhold judgement, except to say, I'm not your grandparents.

Answer 45

There's a subliminal message behind that which implies "Careful not to compare me to your grandparents". You can mis-interpret or mistakenly mis-read someone else's communication style and create unnecessary conflict that way.