Mathematics, 28.01.2020 04:31 lilmackey

Agift bag shaped like a rectangular prism has a volume of 1152 cubic inches. the dimensions of the gift bag in terms of its width are shown. the height is greater than the width. what are the dimensions of the gift bag? length: in., width: in., height: in.

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The answer is
w = 6 in
l = 16 in
h = 12 in

The volume of a rectangular prism with length l, width w, and height h is:
V = l * w * h

V = 1152 in³

After some internet research, I found out that:
l = 2w + 4
h = 18 - w

So,
V = l * w * h
1152 = (2w + 4) * w * (18 - w)

Multiply the first two factors:
1152 = (2w² + 4w) * (18 - w)

Multiply two remaining factors:
1152 = 36w² + 72w - 2 w³ - 4w²

Rearrange:
-2w³ + 36w² - 4w² + 72w = 1152
-2w³ + 32w² + 72w = 1152
-2w³ + 32w² + 72w - 1152 = 0

Divide all by 2:
-w³ + 16w² + 36w - 576 = 0

Multiply by (-1):
w³ - 16w² - 36w + 576 = 0

Rearrange:
(w³ - 36w) - (16w² - 576) = 0

Factor:
w * w² - w * 36 - (16 * w² - 16 * 36) = 0
w(w² - 36) - 16(w² - 36) = 0
(w - 16)(w² - 36) = 0
(w - 16)(w² - 6²) = 0
(w - 16)(w - 6)(w + 6) = 0

So, w - 16 = 0, or w - 6 = 0, or w + 6 = 0.
In other words: w = 16, or w = 6, or w = -6.

Width cannot be negative, so w ≠ -6.
If w = 16, then l = 2 * 16 + 4 = 32 + 4 = 36 and h = 18 - 16 = 2
But, since the height must be greater than the width (h > w), w ≠ 16

If w = 6, then l = 2 * 6 + 4 = 12 + 4 = 16 and h = 18 - 6 = 12.
Thus:
w = 6 in
l = 16 in
h = 12 in

Answer from: ciel8809

The length of the bag is 48in, the width of the bag is 24in and the height of the bag is 48in.

Ractangular prism has 4 sides on its base. The volume of the rectangular is the product of the length of the base, the width of the base, and its height.

Let v be the volume of the prism and l, b and h be the length of the base, the width of the base, and its height respectively. Now volume can be formulated as,

$v=l\times w\times h$

As the dimetions of the gift bag are not given so assume a regular gift bag with a length twice the width and height is equal to its length. therefore

l=2w

$\dfrac{I}{2} =w$

and

l=h

Put the value of width and height in the formula of volume, we get,

$v=l\times \dfrac{l}{2} \times l$

$1152=\dfrac{l^3}{2}$

$l^3=1152\times2$

l^3=3456

$l=\sqrt[3]{3456}$

l=48

The length of the beg is 48 in. As the length is equal to height therefore height is also 48 in. the width is half of the length so the width is 24 in.

Hence, the length of the bag is 48in, the width of the bag is 24in and the height of the bag is 48in.

For more about the prism follow the link below-

link

Answer from: Quest

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf =

pf = 6,25 u

ver más en -

step-by-step explanation:

Answer from: Quest

i believe the answer is 323 ft

step-by-step explanation:

Alarge asteroid crashed into a moon of another planet causing several boulders from the moon to be p

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