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Ann
04/08/2022 07:25:56
you said it already
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Ann
04/08/2022 07:26:01
the length and width of a square are the same
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Ann
04/08/2022 07:26:15
and the area of a rectangle is its length multiplied by its width
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Ann
04/08/2022 07:27:02
i don't know how else to say it
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Angelic
04/08/2022 07:27:20
I’m just not sure what the length or width is
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Ann
04/08/2022 07:27:33
.
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Ann
04/08/2022 07:27:43
> the smaller pool, which is a square **with side length x**
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Angelic
04/08/2022 07:30:05
xlw?
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Ann
04/08/2022 07:30:27
??
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Ann
04/08/2022 07:30:36
what's `l`? what's `w`? where are these new letters coming from?
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Ann
04/08/2022 07:30:39
don't overthink it... please. seriously please don't overthink it, i'm begging you.
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Angelic
04/08/2022 07:33:16
x^2?
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Ann
04/08/2022 07:33:33
yes!!!
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Ann
04/08/2022 07:33:55
i mean like, think about it! why do we call raising something to the second power "squaring"?
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Ann
04/08/2022 07:34:04
it's because x^2 is the area of a **square** with side x!
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Angelic
04/08/2022 07:34:15
Ohhh that makes more sense
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Ann
04/08/2022 07:34:16
does the name not speak for itself?
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Ann
04/08/2022 07:34:26
okay so now that we've gotten past that little block
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Ann
04/08/2022 07:34:32
what's the area of the _bigger_ pool?
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Angelic
04/08/2022 07:35:07
Y^2?
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Ann
04/08/2022 07:35:22
lowercase
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Ann
04/08/2022 07:35:23
but yes, y^2
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Ann
04/08/2022 07:35:30
okay, now:
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Ann
04/08/2022 07:35:30
> The sum of the areas of the two pools is 730 square feet.
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Ann
04/08/2022 07:35:37
can you now write this down as an equation?
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Angelic
04/08/2022 07:36:00
y^2+x^2 = 730
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Ann
04/08/2022 07:36:06
bravo
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Ann
04/08/2022 07:36:23
okay, so now you have your two equations: ``` 4y = 4x + 16 y^2 + x^2 = 730 ```
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Ann
04/08/2022 07:36:32
are you now able to solve these equations for x and y?
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Angelic
04/08/2022 07:38:46
I would not be able to, would I have to use substitution?
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Ann
04/08/2022 07:39:00
you don't "have to" use substitution but it is a decent first step.
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Angelic
04/08/2022 07:40:48
If I would to use substitution would it be (x+4)^2+x^2=730?
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Ann
04/08/2022 07:41:03
that is what equation you'd get after substitution, yes
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Ann
04/08/2022 07:42:45
do i understand correctly that you are now solving the equation (x+4)^2 + x^2 = 730?
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Angelic
04/08/2022 07:43:09
Yes
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Ann
04/08/2022 07:43:33
okay
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Ann
04/08/2022 07:43:38
ping me once you have an answer or are stuck
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Angelic
04/08/2022 07:45:24
Would I be able to get to the next step if I square rooted both sides and getting 2x+4=27~ @Ann
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Ann
04/08/2022 07:45:31
...........
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Ann
04/08/2022 07:45:46
no, you fucked up.
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Ann
04/08/2022 07:45:57
$\sqrt{(x+4)^2 + x^2}$ is NOT the same as $(x+4) + x$.
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TeXit
04/08/2022 07:45:59
**Ann**
https://cdn.discordapp.c…144404037632.png
183668144404037632.png
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Ann
04/08/2022 07:46:13
sqrt(a+b) is not equal to sqrt(a)+sqrt(b).
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Angelic
04/08/2022 07:46:49
What would my next step be then?
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Ann
04/08/2022 07:47:06
your next step would be to recognize that (x+4)^2 + x^2 = 730 is a **quadratic equation** in x.
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Ann
04/08/2022 07:47:10
and act accordingly.
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Ann
04/08/2022 07:47:16
namely, you should first clean it up
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Ann
04/08/2022 07:47:22
i.e. bring it into standard form
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Ann
04/08/2022 07:47:46
and then solve it in any way you like, such as factoring, completing the square, or the quadratic formula.
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Ann
04/08/2022 07:48:12
and if you do not remember how to solve quadratic equations at all then you really should go give that a review, because that roadblock is not something that can be overcome in a single discord chat.
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Angelic
04/08/2022 07:48:52
I remember those methods but for me either completing the square or the quadratic formula is the easiest
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Ann
04/08/2022 07:49:11
i don't like repeating myself, but again, the exact method doesn't matter.
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Angelic
04/08/2022 07:49:20
Alright
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Angelic
04/08/2022 07:51:01
The standard form of (x+4)^2 would be x^2+8x+16 correct?
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Ann
04/08/2022 07:51:29
(x+4)^2 expands to x^2 + 8x + 16, yes.
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Angelic
04/08/2022 07:52:05
And then you add x^2 onto that which would give you 2x^2 + 8x + 16?
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Angelic
04/08/2022 07:52:13
Or did I mess something up?
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Ann
04/08/2022 07:53:17
no, nothing so far.
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Ann
04/08/2022 07:53:31
you have rewritten the equation as `2x^2 + 8x + 16 = 730`. so far so good.
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Angelic
04/08/2022 07:54:04
Could I be able to divide both sides by 2? That would still equal the same thing right?
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Ann
04/08/2022 07:54:18
"could i be able"...
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Angelic
04/08/2022 07:54:35
So I get something like x^2 + 4x + 8 = 365
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Ann
04/08/2022 07:54:35
yes, you CAN always divide both sides by 2. that's not something you need special permission for.
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Ann
04/08/2022 07:54:39
not "something like"
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Ann
04/08/2022 07:54:45
you get _exactly_ that, no more and no less
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Angelic
04/08/2022 07:54:52
Yes mam
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Angelic
04/08/2022 07:57:21
From there I could do -8 from both sides and then take half of b and square it, then add that to both sides, factor the left side and then square root both sides
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Angelic
04/08/2022 07:57:36
Is that correct or did I mess up something along the way
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Angelic
04/08/2022 07:57:39
@Ann
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Ann
04/08/2022 07:58:14
would appreciate if you showed your work
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Angelic
04/08/2022 07:58:41
Alright let me do that, I’ll be right back
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.,..
04/08/2022 07:58:54
quadratic formula should do the trick
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Ann
04/08/2022 07:59:01
ping me once you're back.
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Angelic
04/08/2022 08:18:03
So I’m back @Ann
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Ann
04/08/2022 08:18:11
uh huh
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Angelic
04/08/2022 08:18:29
The final equation I’ve come to is x = -2 + or - 19
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Ann
04/08/2022 08:19:02
$x = -2 \pm 19$?
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04/08/2022 08:19:05
**Ann**
https://cdn.discordapp.c…144404037632.png
183668144404037632.png
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Ann
04/08/2022 08:19:06
yes, that sounds right.
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Angelic
04/08/2022 08:19:12
Yeah
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Ann
04/08/2022 08:19:31
now remember what x represented, and you should see that one of these solutions will have to be discarded and the other solution is your goal.
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help-10
8e2a51bd6df549688fe8c944b1bd183b
262,130,879,873,286,140
Angelic
04/08/2022 08:19:46
It can’t be a negative if I’m correct
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help-10
8e2a51bd6df549688fe8c944b1bd183b
262,130,879,873,286,140
Angelic
04/08/2022 08:19:53
So x = 17 has to be the answer
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help-10
8e2a51bd6df549688fe8c944b1bd183b
183,668,144,404,037,630
Ann
04/08/2022 08:19:53
it's a length.
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help-10
8e2a51bd6df549688fe8c944b1bd183b
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Ann
04/08/2022 08:19:57
so yes, x cannot be negative.
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help-10
8e2a51bd6df549688fe8c944b1bd183b
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Ann
04/08/2022 08:20:09
and since you were asked for the length of the smaller pool, you need not do anything else.
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help-10
8e2a51bd6df549688fe8c944b1bd183b
183,668,144,404,037,630
Ann
04/08/2022 08:20:22
but for the sake of completeness, i would like you to say now what the length of the _bigger_ pool is too
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help-10
8e2a51bd6df549688fe8c944b1bd183b
262,130,879,873,286,140
Angelic
04/08/2022 08:23:27
Alright
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8e2a51bd6df549688fe8c944b1bd183b
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Angelic
04/08/2022 08:23:30
I will do that
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8e2a51bd6df549688fe8c944b1bd183b
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Angelic
04/08/2022 08:24:53
Alright
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Ann
0413
Ann
false
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8e2a51bd6df549688fe8c944b1bd183b
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Angelic
04/08/2022 08:24:55
I finished
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8e2a51bd6df549688fe8c944b1bd183b
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Angelic
04/08/2022 08:25:06
I got that the length of the bigger pool is 21 ft @Ann
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Ann
04/08/2022 08:26:06
that is correct
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8e2a51bd6df549688fe8c944b1bd183b
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Angelic
04/08/2022 08:26:18
I just plugged in 17 for x in y^2 + x^3 = 730 and jsut solved it from there
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f0ece9b1ebe94d7f8753fa2c905cc94f
801,708,790,981,984,300
aaron_
11/12/2021 05:31:42
Second Quarter DLP 1 Directions: A. Find the quotient. Differentiate the quotient as terminating or repeating decimal by putting a check (/) under the corresponding column. Equation Quotient Terminating Repeating Ex. 5 ÷ 15 = 0.33̅ √ 1. 3 ÷ 15 = 2. 4 ÷ 45 = 3. 9 ÷ 12 = 4. 8 ÷ 12 = 5. 2 ÷ 4 = B. Give the equivalent valu...
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Ann
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8dd27e1ab4fd464fab1c6fc3e6e17987
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Ann
04/08/2022 08:35:51
you didn't really need to do that
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8dd27e1ab4fd464fab1c6fc3e6e17987
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Ann
04/08/2022 08:35:55
...oh
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8dd27e1ab4fd464fab1c6fc3e6e17987
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Ann
04/08/2022 08:35:57
god damn it
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8dd27e1ab4fd464fab1c6fc3e6e17987
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Ann
04/08/2022 08:36:02
but anyway yeah you did not need to do that
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help-10
8dd27e1ab4fd464fab1c6fc3e6e17987
183,668,144,404,037,630
Ann
04/08/2022 08:36:11
you could have just used the equation y = x + 4 that you already had
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