Question

is my answer correct?

Answer 1

Hard to tell so far :-)

Answer 2

2498

Answer 3

haha sry

Answer 4

Show me your work...

Answer 5

ok

Answer 6

2225-2030/50-20=6.5

Answer 7

then

Answer 8

2030=6.5*20+b

Answer 9

b=2160

Answer 10

Wait, aren't you supposed to find the weight of the plane when it has 62 gallons of fuel? Seems like you need to use "62" somewhere in the process :-)

Answer 11

6.5(62)+2160=2563

Answer 12

my first answer was wrong

Answer 13

it was lagging

Answer 14

so my answer that i think it might be correct is 2563

Answer 15

I agree with your computation of the weight of a single gallon of fuel. But what you are doing with it doesn't convince me yet. What is the weight of the airplane with no fuel?

Answer 16

we know that the weight with 20 gallons is 2030 lbs. we know a gallon weighs 6.5 lbs. we want to know weight when 62 gallons on board, so we can either a) find the weight of the empty airplane, add the weight of 62 gallons, or b) add the weight of 62-20 = 42 gallons to the weight of the plane with 20 gallons already on board.

Answer 17

42*6.5 = 273. 2030+273 = ?

Answer 18

2303

Answer 19

yeah I thought my number was to high lol

Answer 20

Right.

Answer 21

thanks

Answer 22

hey you know about graphing ?

Answer 23

Worth looking back at what you did and figuring out what the mistake was...know your enemies :-)

Answer 24

Well, I've drawn and read a few in my time...

Answer 25

can you help me with this one

Answer 26

Find the equation of a circle whose diameter has endpoints (-2,1) and (6,3). Seems like there might actually be two circles that meet that description :-)

First we want to find the length of our diameter. Do you remember the formula for the distance between two points?

Answer 27

Not fromt the top of my head lol

Answer 28

by getting the radius

Answer 29

which the radius is 3

Answer 30

The distance formula is just the Pythagorean theorem in disguise.

\[d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\] where the two points are \((x_1,y_1)\) and \((x_2,y_2)\). It doesn't matter which point is which, because of the squaring.

Answer 31

right

Answer 32

Having found the distance between the two points, we would divide it in half to get the radius, as you suggest.

Answer 33

x1+x2/2

Answer 34

No, not that easy, we could only do that if the two y values were identical.

Answer 35

y1+y2/2

Answer 36

oh okay

Answer 37

Now, if you wanted, you could find the midpoint of the diameter, and then find the distance to either endpoint and that would be the radius, but that's more work than dividing a number by 2, I think :-)

Answer 38

well i got it and both are 3

Answer 39

but keep talking, i might be wrong (most possibly)

Answer 40

huh, are you sure?

Answer 41

how did you arrive at that figure?

Answer 42

by x1+x2/2=3
y1+y2/2=3

Answer 43

You might want to check your arithmetic a little more carefully there :-)

Answer 44

Also, that's finding the midpoint of the line, not its length.

Answer 45

oops hahah my bad

Answer 46

sry x1+x2/2=1

Answer 47

not 3

Answer 48

And neither of them = 3. (6 + (-2)) = 4, divide by 2 you get 2. Similarly, 3+1 = 4, divide by 2, you get 2.

So our two endpoints are \((x_1=6, y_1=3)\) and \((x_2=-2,y_2=1)\)

Distance formula gives:
\[d = \sqrt{(6-(-2))^2 + (3-1)^2} =\]

Answer 49

(you tell me)

Answer 50

k im back sry

Answer 51

okay

Answer 52

12

Answer 53

mmm...no. that would mean that the quantity under the square root sign was 144, and I don't see how you get that..

Answer 54

What is 6 - (-2)?

Answer 55

oops sry

Answer 56

8

Answer 57

No need to apologize to me, apologize to yourself!

Answer 58

Yes, so 8^2 = ?

Answer 59

64

Answer 60

right. (3-1)^2 = ?

Answer 61

4

Answer 62

68

Answer 63

64 + 4 = 68 square root of 68 =?

Answer 64

2sqrt17

Answer 65

right! Now that the diameter, so the radius is half of that, or sqrt 17. Great.

Now we need to find the center of that diameter, and that is (2,2) as you previously determined. So, we have a circle with radius sqrt (17), and center 2,2. Do you know the general formula for a circle?

Answer 66

no

Answer 67

actually, the formula for a circle centered at the origin will do just fine, too.

Answer 68

maybe except i dont remmember

Answer 69

okay, circle at the origin with radius 1 is \(x^2 + y^2 = 1\).

Answer 70

Think about that for a second: that circle will go through points (1,0), (0,1), (-1,0), and (0,-1), right?

Answer 71

how?

Answer 72

One end of the radius is at (0,0) and the other sweeps around, touching all the points that are exactly 1 away.

Answer 73

And as it touches each of the x and y axis crossings, those will be the points at which it does so, right?

Answer 74

oh okay