Question

@mathstudent55 Hi i have been asking for help could please help me again?

Answer 1

I can try.

Answer 2

Thank you..

Before blast-off, the Mathonauts must set the trajectory of their ship. Create a linear equation with a positive slope to be your original trajectory.

I have the linear equation y=2x+1 so what do you think do you think i should change it.

Answer 3

You have come up with a linear equation with a positive slope.
That's what you were asked to do.

What is the next instruction?

Answer 4

After blast-off, the sensors have picked up an incoming meteor. The Mathonauts frantically start preparing for impact. If the linear equation of the meteor’s path is known, describe to the captain how to solve where your equation from question 1 and the meteor’s path will cross. Explain any possible methods used in discovering a solution.

Answer 5

Use elimination

Answer 6

elimination method is done by ADDING both equations vertically, once all variables are aligned let's say the meteor's path is y = -2x +25 so y = 2x + 1 y = -2x + 25 ------------ 2y = 0 + 26 and you can see right off what "y" would be, then you'd get "x" by substituting "y" on either equation by ADDING the equations vertically like so, you're in fact ELIMINATING one of the variables
now, if you GRAPH both equations and the graphs touch each other or INTERSECT the solution is the (x, y) coordinate values at that INTERSECTION POINT that'd be the other way

Answer 7

Since the meteor is also governed by a linear equation, you have a system of two linear equations.
Here are some methods you can use to solve the system of equations:
1. Substitution
2. Addition

Answer 8

Ok what yesterday was when i use y=2x+1 and -2x+10 i got 2y=0+11..

Answer 9

that was elimination should i do it with substitution..

Answer 10

@mathstudent55 What do you think?

Answer 11

***
y=2x+1 and -2x+10 i got 2y=0+11.
***

I assume you mean
y=2x+1 and
y = -2x + 10

yes, you get 2y=0+11
which can be simplified to 2y = 11
and (divide both sides by 2)
y= 11/2 (or 5.5)

Answer 12

next, find x using either of your two equations.
example:
y= 2x+1
when y = 11/2 you get
11/2 = 2x + 1

add -1 to both sides
11/2 -1 = 2x +1 -1

simplify to
11/2 - 2/2 = 2x

can you finish to find x ?

Answer 13

is it 9/4

Answer 14

@phi you there i got x=9/4

Answer 15

yes. x= 9/4

that means the two lines meet at
(9/4, 11/2)

Answer 16

ok thank you

Answer 17

what about this one .

Having survived the meteor impact, thanks to some last-minute evasive maneuvers, the Mathonauts now set their sights on their Interstellar Headquarters. The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the original trajectory of the ship and complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path.

Answer 18

this newest equation is a circle (it matches x^2 + y^2 = r^2 )
\[ x^2 + y^2 = 200^2 \]

they are asking you to find where the line
y=2x+1
intersects the circle.

Answer 19

you could use substitution.

Answer 20

how do you do it..is it you put 2 in the place of x equal to 2x2

Answer 21

you know y = 2x+1

in other words, y and (2x+1) are the same thing.
replace y in
x^2 + y^2= 40,000

Answer 22

so do i do (2x+1)2+y2=40,000

Answer 23

almost. but you replace the y (you replaced x with (2x+1) which is not correct)

Answer 24

so how should i do it?

Answer 25

in other words, you want
\[ x^2 + (2x+1)^2 = 40000 \]

Answer 26

so now i have to foil it

Answer 27

yes. then "combine like terms"
to get a quadratic equation (in the form a x^2 + b x + c=0 )

and because these are messy numbers, you will have to use the quadratic formula and a calculator to solve for x

Answer 28

im going to do it and i will tell you what i get in a minute.

Answer 29

post the results as you go ... because this takes a lot of steps to get to the final x answer, and it's easier to check things as we go.

Answer 30

i do parentheses first x2(2x+1)2 = x2(2x+2)=40000 so x2 time x2= 2x3 x2 time 2 =2x2 so i got 2x3+2x2=40,000 i think im doing sothing wrong what do you think

Answer 31

\[ x^2 + (2x+1)^2 = 40000 \]

remember that "squaring" means multiply by itself, so this is the same as
\[ x^2 + (2x+1)(2x+1) = 40000 \]

just concentrate on this part:
\[ (2x+1)(2x+1) \]
use FOIL

Answer 32

I forgot that so x2+4x2+2x+2x+=40,000 so combine like terms x2+4x2+4x=1=40,000

Answer 33

so 2x+4x2= 5x2+1=40,000

Answer 34

equations only have 1 equal sign
you mean
\[ x^2+4x^2+4x+1=40,000\]
btw, you should use ^ to show the 2's are exponents

Answer 35

you can combine the x^2 terms and get
\[ 5x^2 + 4x + 1 = 40000\]
add -40000 to both sides and simplify to get
\[ 5x^2 + 4x - 39999=0 \]

Answer 36

this video explains how to solve this
http://www.khanacademy.org/math/algebra/quadratics/quadratic-formula/v/using-the-quadratic-formula

Answer 37

you need to know how many batteries each type needs

if you name the number of missiles "x"
and the number of ray-guns "y"
then

The ship can hold only 15 weapons total
means the sum of missiles and guns is 15. i.e. x+y=15

if we know how many batteries a missile uses (call the number of batteries "a")
and we knew the guns needed "b" batteries, then
The ship only has 45 batteries.
means a x + b y ≤ 45

but we need numbers for a and b to solve this.