Question

gwhrwhy

Answer 1

@phi

Answer 2

i have the two pieces as x and 30-x. (1/3)x is the length of each side of the triangle and the length of each square side is (30-x)/4

Answer 3

@RadEn

Answer 4

so far so good. Now you need the formula for the combined area

Answer 5

@phi i simplified it till (1/16)(x^2+(4x/sqrt3)-60x+900). i just don't know how to do -b/2a

Answer 6

@phi?

Answer 7

yes, you would use -b/2a

but I don't believe your formula for the total area.

Answer 8

what do you think it is then?

Answer 9

area for an equilateral triangle is sqr(3)/4 * x^2
area of a square is x^2 (in this case (30-x)^2 )

Answer 10

wouldn't the are of the square be ((30-x)/4)^2 because each side is 30-x/4? 30-x is the total length of the second piece of string

Answer 11

yes, ( (30-x)/4 )^2 for the square

and sqr(3)/4 (x/3)^2 for the triangle.

Answer 12

ok so what would the total are be then now?

Answer 13

can you work it out ?

Answer 14

i think give me a sec

Answer 15

A=(1/6)((900-60 x+x^2+(4 x^2)/sqrt(3))?

Answer 16

you mean 1/16 not 1/6 , right ?
and x is the length of the string used to make the triangle. its side is x/3

Answer 17

sorry yeah 1/16. yes the side is x/3

Answer 18

the area of the triangle should be
sqr(3)/4 * x^2/ 9 = sqr(3) x^2 / 36
(I would leave the sqr(3) up top)

Answer 19

ok so what would the total area be now

Answer 20

distribute the 1/16, and collect terms

you want to write down the equation of a parabola in the form

ax^2 + bx + c

so you can find its vertex (= -b/(2a) )

Answer 21

but isn't my equation wrong?

Answer 22

start with
A = 1/16(x^2 -60x + 900) + sqr(3) x^2 / 36

Answer 23

ok so it's (1/16)x^2-15/4x+225/4+sqr(3)x^2/36

Answer 24

you should combine the x^2 terms

Answer 25

(x^2/16+x^2/(12 sqrt(3)))

Answer 26

you want a coefficient in front of x^2 so you can use it in -b/(2a)

maybe you should change everything to decimals?

Answer 27

or i could do (1/16+1/12sqrt3)x^2 right?

Answer 28

yes. so a = (1/16+1/12sqrt3)

but you will need a calculator to find a decimal equivalent of that mess.

I would answer with a decimal number, unless the question is multiply choice in a different format.

Answer 29

ok sure. and b=-15/4?

Answer 30

btw, most people leave square roots in the top of a fraction (and never in the bottom)
(before the invention of calculators, dividing by a square root was *way hard* so people never left a square root in the bottom)

and yes, b = -15/4

Answer 31

ok so -b/2a=(60(4sqrt3-3))/13=18.13

Answer 32

what did you get for a?

Answer 33

a=a = (1/16+1/12sqrt3) and aslo i did it wrong. i for got the 2a part
-b/2a=(30(4sqrt3-3))/13

Answer 34

a should be (1/16 + sqr(3)/36)

Answer 35

or (1/16 + 1/(12 sqr(3) ) )

Answer 36

yeah thats what i did

Answer 37

-b is 3.75

Answer 38

the answer is not 18.03 or 9...

Answer 39

ok but is my -b/2a=(30(4sqrt3-3))/13 correct?

Answer 40

no

Answer 41

then what should it be?

Answer 42

You almost have the answer. Just focus and work on it.

Answer 43

what am i doing wrong?

Answer 44

at least tell me this

Answer 45

@sourwing

Answer 46

@jdoe0001 @campbell_st @robtobey