Question

Danielle is playing the newest app on her phone, Algebra City Defense. Earlier in the game, you and Danielle helped the Mathonauts defend the city against a giant, three-headed monster. After defeating the monster, the game advances to Level Two! You and Danielle must help the Mathonauts blast off to their Interstellar Headquarters.

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.

Answer 1

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 2

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 3

give me a sec

Answer 4

thank you

Answer 5

no prob

Answer 6

1. 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.
y = 4x + 18

2. 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.

3. 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.

4. While docked, the captain wants to resupply the ship’s missiles and ray-guns. You will need to
explain to the captain what information you must know and how that can be used to determine the number of missiles and ray-guns to fill the ship and use all the batteries.
The ship can hold only 15 weapons total and only has 45 batteries.
The missiles and ray-guns each require different amounts of batteries to operate.

5. Before departing the Interstellar Headquarters, the ship’s navigator begins to plan the next trip. She uses a map with their current trajectory already graphed on it. There is also a table that has coordinate points of a satellite that the Mathonauts must intercept. Explain to the navigator how she can use the graph and table to find where they will intercept the satellite.

Answer 7

does that help at all?

Answer 8

a little.. im horrible with word problems so can u explain more?

Answer 9

well im not that great myself by i will try to help

Answer 10

ok so you know what your slope is?

Answer 11

yes

Answer 12

what is it?

Answer 13

slope of a line like /

Answer 14

no in the answer i sent you i gave you the slope what is it?

Answer 15

the equation

Answer 16

can u please tell me what the equation is?

Answer 17

y = 4x + 18

Answer 18

Good! :)

Answer 19

ok nowdo you know what is next on the list?

Answer 20

figure out how to not get hit and use the slope of the ships path and path of meteor

Answer 21

yea

Answer 22

okay but it doesnt tell me the path of the meteor

Answer 23

ok are there two ships or one?

Answer 24

one i think

Answer 25

is this geometry ?

Answer 26

You can use the substitution method. You find what Y or X equals in one of the equations first. Next you substitute the value of Y or X, whichever one you solved in the first step. Once you find the numerical value of Y or X, you plug the value back into one of your original equation and solve for the missing value you do not have yet.

Answer 27

You can substitute your original trajectory (y=5x+1) into the equation that the Interstellar Headquarters is based on (y2+x2=40,000). You will be with the equation 2(5x+1)+x2=40,000 and you will solve for X. After solving for X, you will have X=3333.12 for your value. You will now take this value back into one of your original equations. You will now have the equation y=5(3333.17)+1 and will solve for Y. Your value for Y will be Y=16666.85. You now know the ship’s path will cross the Interstellar Headquarters’ at the coordinate (3333.17, 16666.85).

Answer 28

You will need to know how many batteries it takes to run the missiles and ray-guns. Once you have this information you can then find out all the different combinations of missiles and ray-guns you can have on your ship.

Answer 29

does this help anymore than before?

Answer 30

thanks

Answer 31

yes this helps alot can we continue?