Question

NEED HELP!!MEDAL AND FAN!!!
A construction engineer needs to make 25 square concrete slabs with sides of length x feet and a height x - 3 feet. If the engineer can use at most 350,000ft^3 of concrete, what should the dimensions of each slab be, to the nearest foot?
a. Write an expression for the volume of all the slabs
b. What should x equal, to the nearest foot?

Answer 1

@campbell_st @dan815

Answer 2

@jim_thompson5910

Answer 3

-3

Answer 4

what?

Answer 5

@BRONCOBURDEN17 @jim_thompson5910

Answer 6

please help

Answer 7

@horsegirl27

Answer 8

so reading the question is the side lengths are x and the height is x.

base area of a slab is A = x * x

multply by the height x -3 to find the volume of 1 slab

so if you make 25 slab

the total volume will be 25 * volume of 1 slab

hope that makes sense

Answer 9

not really :(

Answer 10

so the volume for 25 can be equated to the total volume

Answer 11

i still dont understand

Answer 12

`square concrete slabs with sides of length x feet and a height x - 3 feet.`

each slab looks like this

Answer 13

ok

Answer 14

what is the volume of one slab?

Answer 15

it shows that picture

Answer 16

idk the volume

Answer 17

multiply out the dimensions

Answer 18

volume = length*width*height

Answer 19

3x-3

Answer 20

?

Answer 21

what is x times x equal to?

Answer 22

2x

Answer 23

no

Answer 24

x+x = 2x

Answer 25

x*x = x^2

x^2 = x squared

Answer 26

x^2

Answer 27

x^3-3?

Answer 28

so we have x^2 times (x-3)

multiply the x^2 by x to get x^3
multiply the x^2 by -3 to get -3x^2

Answer 29

so x^2*(x-3) = x^3 - 3x^2

Answer 30

`x^3 - 3x^2` is the volume of ONE slab

but we have 25 of them all together

Answer 31

would that be the expression for part a ?

Answer 32

a. Write an expression for the volume of all the slabs
b. What should x equal, to the nearest foot?

Answer 33

it's close to the answer, but not quite there. Carefully re-read my last post

Answer 34

oh okay. x^3 - 3x^2 * 25?

Answer 35

25 times the whole group, so you use parenthesis

Answer 36

25*(x^3 - 3x^2)

distribute to get

25*(x^3 - 3x^2) = 25x^3 - 75x^2

Answer 37

`25x^3 - 75x^2` is the volume of 25 slabs

Answer 38

ok is that the final expression?

Answer 39

for the 25 slabs, yes that's the total volume

Answer 40

okay now how do i solve?

Answer 41

?

Answer 42

set 25x^3 - 75x^2 equal to 35,000 and solve

25x^3 - 75x^2 = 35,000
25x^2(x - 3) = 35,000
x^2(x - 3) = 35,000/25
x^2(x - 3) = 1,400
x^3 - 3x^2 = 1,400
x^3 - 3x^2 - 1,400 = 0

At this point, use a graphing calculator to solve for x

Answer 43

i dont understand. can u go step by step?

Answer 44

you type in x^3 - 3x^2 - 1,400 into a calculator at this point. Do you have one?

Answer 45

yea
hang on

Answer 46

-1400?

Answer 47

what kind of calculator do you have?

Answer 48

i have a ti-30xa so i used the website http://www.meta-calculator.com/online/?panel-201-calculator

Answer 49

ok desmos is probably a better grapher

https://www.desmos.com/calculator

Answer 50

type in `x^3 - 3x^2 - 1400` and find out where it crosses the x axis

Answer 51

12.28?

Answer 52

oh my bad, I used 35,000 when it should be 350,000

350,000/25 = 14,000

Answer 53

type in `x^3 - 3x^2 - 14000` instead

Answer 54

25.14?

Answer 55

yes, which rounds to x = 25

so that's the largest x can get

Answer 56

ok thanks!

Answer 57

yw