Quadratic Relations [+rep]

[Maki]

Here I am again with this stupid quadratics hubbub

1. Pauline wants to sell stainless steel bottles at a school fundraiser.
She knows that she will maximize profits and raise $1024 if she sells the bottles for $28 each.
She also knows that she will lose $4160 if she sells the bottles for $10 each.
White a quadratic relation to model her profit, P, in dollars if she sells the bottles for x dollars each.
------------------
vertex (28, 1024)
point (10, 4160)

y = a (x-28) + 1024

That's all I have so far for that question...not sure what else to do. I tried subbing in (10, 4160) but I didn't get the answer on the back of the book which is y = -16 (x-28)^2 + 1024

2. Water from a fire hose is sprayed on a fire that is coming from a window. The window is 15m up the side of a wall. The eqn H = -0.011x^2 + 0.99x + 1.6 models the height of the jet of water, H, and the horizontal distance it can travel from the nozzle, x, both in metres.
How far back could a firefighter stand but still have the water reach the window?

Tried finding the zeros of the relation, but no dice. The answer says 16.66 or 73.4m

+fullrep if you thoroughly help me please I'm desperate I have a final tomorrow and it makes me angry I don't understand these STILL

[Poem]

@(you need an account to see links) I'm almost 100% sure the book is wrong. What you did was correct.

Otherwise:

y = a (x-28)^2 + 1024
-4160 = a (-14)^2 + 1024
-5184 = 196a
a = -26.5

The book probably messed up on algebra and added 1024 on the left side instead of subtracted. If you make that mistake then you get -16


EDIT: just noticed there was a question 2, working on it rn[COLOR="Silver"]

---------- Post added at 10:56 PM ---------- Previous post was at 10:52 PM ----------

[/COLOR @(you need an account to see links)

H = -0.011x^2 + 0.99x + 1.6

Set H = 15 since you want to find the farthest. (If H is above 15 it means you can still move farther, and if H is below 15, well, you're not satisfying the conditions in the question)

15 = -0.011x^2 + 0.99x + 1.6
0 = -0.011x^2 + 0.99x - 13.4

Solve for x using the quadratic formula, you get 16.6 and 73.4

[Maki]

@(you need an account to see links) I'm almost 100% sure the book is wrong. What you did was correct.

Otherwise:

y = a (x-28)^2 + 1024
-4160 = a (-14)^2 + 1024
-5184 = 196a
a = -26.5

The book probably messed up on algebra and added 1024 on the left side instead of subtracted. If you make that mistake then you get -16


EDIT: just noticed there was a question 2, working on it rn[COLOR="Silver"]

---------- Post added at 10:56 PM ---------- Previous post was at 10:52 PM ----------

[/COLOR @(you need an account to see links)

H = -0.011x^2 + 0.99x + 1.6

Set H = 15 since you want to find the farthest. (If H is above 15 it means you can still move farther, and if H is below 15, well, you're not satisfying the conditions in the question)

15 = -0.011x^2 + 0.99x + 1.6
0 = -0.011x^2 + 0.99x - 13.4

Solve for x using the quadratic formula, you get 16.6 and 73.4

YAY Thank you!!

Can you do one more pleaseeee, it's stumped even @(you need an account to see links)

Nick has a beautiful rectangular garden which measures 3m by 3m.
He wants to create a uniform border of river rocks around three sides of his garden. If he wants the area of the border and the area of the garden to be equal, how wide should the border be?

Ans is 0.84m

[Poem]

YAY Thank you!!

Can you do one more pleaseeee, it's stumped even @(you need an account to see links)

Nick has a beautiful rectangular garden which measures 3m by 3m.
He wants to create a uniform border of river rocks around three sides of his garden. If he wants the area of the border and the area of the garden to be equal, how wide should the border be?

Ans is 0.84m

NP! ^_^

As for your new question:

Let w be the width of border.

The area of garden is 9 m.

We can draw a diagram with the rocks and the garden (NOTE: DIAGRAM SEVERELY NOT TO SCALE )



The border must be 9

So adding all the little rectangles up:
3w + w^2 + 3w + w^2 + 3w = 9

w^2 + 9w = 9
2w^2 + 9w - 9 = 0

Now it should be very easy to solve, just take the positive value which is 0.84 something

[Raj]

@(you need an account to see links) me and mint are both lookin at this one, and we're hella confused about this

So adding all the little rectangles up:
3w + w^2 + 3w + w^2 + 3w = 9

where did you get the 3w and the w^2 from? Can you point that out on your diagram?

EDIT NEVER MIND WE SEE IT

[|2eap]

@(you need an account to see links) me and mint are both lookin at this one, and we're hella confused about this



where did you get the 3w and the w^2 from? Can you point that out on your diagram?

3*w + w*w
add up the outside border its to represent the stone rocks.
so its the area of it all knowing that 3 portions will have atleast a length of 3 since its the dimensions of the garden and then the two corner pieces will be w*w or w^2
and in that equation you solve for w since the 9 is what the area of it is suppose to be.

---------- Post added at 09:31 PM ---------- Previous post was at 09:30 PM ----------

@skarl your random spec on ur diagram made me think i had a mark on my computer and i just scratched it for like 5 minutes trying to get it off -______-

[Raj]

@skarl your random spec on ur diagram made me think i had a mark on my computer and i just scratched it for like 5 minutes trying to get it off -______-

lmao thats poem not skarl

and anyway ty man but we got it a few seconds after i posted that LOL

[Poem]

@skarl your random spec on ur diagram made me think i had a mark on my computer and i just scratched it for like 5 minutes trying to get it off -______-

mspaint woes


@(you need an account to see links) no problem glad you figured it out ^_^

[|2eap]

well thats awk.

[Maki]

@(you need an account to see links) ilyyyyyy ill +rep for this question again when I get the chance!