Writing an equation from a word problem?

Question

Okay...I feel stupid, but I'm bad at understanding stuff. Right now we're working with polynomials. Anyone want to help? please? So here's what I need:

"...a rectangular solid whose height is two feet shorter than its width, and whose length is twice its width. The car has a volume of 150 cubic feet.
Write an expression for the car's volume."

Please don't laugh at me for being dumb...
Thanks people : )

Answer 1

Remember that the volume of a rectangular solid is length times width times height. Therefore, if L = length, W = width, and H = height,

V = LWH

Let's see what we are given:

"The car has a volume of 150 cubic feet"
Therefore, V = 150

"Height is two feet shorter than its width"
"Length is twice its width"

Notice that both the height and length are being compared to the width; based on this standard of comparison, we let W be the variable to work with. Then

L = 2W {length is twice its width}, and
H = W - 2 { height is two free shorter than its width }

So our volume, which is

V = LWH

becomes, after substitution

150 = [2W]W[W - 2]

Which we now use algebra for.

150 = 2W^2 [W - 2]
150 = 2W^3 - 4W^2

Dividing both sides by 2, we get

75 = W^3 - 2W^2

And moving the 75 to the right hand side,

0 = W^3 - 2W^2 - 75

Trial and error, plus long division, will prove the bottom factorization. I've essentially skipped steps at this point.

(W - 5)(W^2 + 3w + 15) = 0

The second set of brackets has no solutions, so we can divide by it and get

W - 5 = 0, or
W = 5

We can now get the length, width, and height, now that we know W.
L = 2W = 2(5) = 10
W = 5
H = W - 2 = 5 - 2 = 3

Answer 2

here's a little help, what do we have?

height: 2 ft shorter than width
length: twice width
volume of car is 150 cubic ft.

so let's call width x. (and height: h, length: l.)

we have
h= x-2
l=2x
w=x

we find volume by multiplying all of these together.

h*l*w=(x-2)(2x)(x)
=(x-2)(2(x^2))
= 2(x^3)-4(x^2)

that's a formula for our volume which is 150 cubic ft... sooooo

150 cubic ft = 2(x^3)-4(x^2)

Answer 3

You aren't DUMB for trying to learn. Don't evere let anyone make you think or feel otherwise.......k? :)

You're smart for asking for help, and smart for asking for only what you need rather than have someone else do it all for you.

As for your question....what does the rectangular solid have to do with the car?

You gave the volume of the car in the problem.......150 cubic feet.

I'm confused I guess. Can you clarify this some?

Answer 4

Let w = width
Then.height = h = w-2
And length = l =2w
So volume =l*w*h = 150 ft^3
Now substitute 2w for l and w-2 for h giving you
Volume = V = 2w*w*(w-2) = 150 ft^3
V = 2w^2(w-2) = 150

You are not dumb. You just haven't had enough studying.

Answer 5

Assume that width = w, length = l, height = h
h = W -2
l = 2*W

Volume = W * h * l
w * (w-2) * 2*w = 150

Answer 6

h = height
w = width
L = length (in feet)

150 = hwL

h = w-2
h+2 = w

L = 2w
L/2 = w

h + 2 = L/2
2h + 4 = L

150 (which is the volume) = h ( h+2 ) ( 2h + 4)
150 = (h^2 + 2h)(2h + 4)
150 = 2h^3 + 4h^2 + 4h^2 + 8h
150 = 2h^3 + 8h^2 + 8h

Answer 7

h: height of car
h + 2: width of car
2(h+2):length

h(h+2)2(h+2) = 150
2h(h+2)^2=150

2h^3+8h^2+8h=150

That's the expression.

The solution is:

h=3 if you wanted to know.

So the height is: 3 feet
The width is: 5 feet
and the length is: 10 feet

Answer 8

I dont know

a rectangular solid whose height is two feet shorter than its width, and whose length is twice its width. The car has a volume of 150 cubic feet.
Write an expression for the car's volume."
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I dont no
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Please don't laugh at me for being dumb...
Thanks people : )
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oh dont feel bad I dont no the answer

Answer 9

a million. (2)(8x-5) 2. (2)(5y-10) 3. 12x-30 right here they are, the first 2 are only doubling, so that you're taking a the variety (or this situation the equation) and multiply by using 2. third you're taking the salary, and multiply it by using the type of hours you paintings. and then take that result and subtract 30. desire I helped.

Answer 10

Okay so volume is l*w*h and we know that l*w*h=150

So let width = x (because everything is always x in this kind of thing, but it can be whatever letter you want)

l=(2x)
w=x
h=(x-2)

so
(2x)(x)(x-2)=150