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3 years ago

A rectangular field is nine times as long as it is wide. If the perimeter of the field is 1700 feet, what

Mathematics

1 answer:

Leokris [45]3 years ago

6 0

Answer:

I. L = 10.35 feet

II. W = 93.15 feet.

Step-by-step explanation:

Let the length of the rectangle be L.

Let the width of the rectangle be W.

Given the following data;

Perimeter of rectangular field = 1700 feet

Translating the word problem into an algebraic expression, we have;

W = 9L

Mathematically, the formula for the perimeter of a rectangle is;

P = 2(L + W)

A. To write an equation;

X = P = 2(L + W)

B. To find the dimensions of the field;

207 = 2(L + 9L)

207 = 2L + 18L

207 = 20L

L = 207/20

L = 10.35 feet

To find the weight;

W = 9L

W = 9 * 10.35

W = 93.15 feet.

Therefore, the width of the field is

93.15 feet and the length of the field is

10.35 feet.

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Answer:

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Step-by-step explanation:

Aquí tenemos que comprar el frasco que tiene el menor costo por volumen.

$h_1$ = Altura del frasco corto

$h_2$ = La altura del frasco alto es el doble que el del frasco corto. = $2h_1$

$d_1$ = Diámetro del frasco corto

$d_2$ = El diámetro del frasco alto es la mitad del frasco corto = $\dfrac{1}{2}d_1$

El volumen de un cilindro es $\pi \dfrac{d^2}{4}h$

La razón de los volúmenes de los frascos es

$\dfrac{V_1}{V_2}=\dfrac{\pi\dfrac{d_1^2}{4}h_1}{\pi\dfrac{d_2^2}{4}h_2}\\\Rightarrow \dfrac{V_1}{V_2}=\dfrac{d_1^2h_1}{d_2^2h_2}\\\Rightarrow \dfrac{V_1}{V_2}=\dfrac{d_1^2h_1}{(\dfrac{1}{2}d_1)^22h_1}\\\Rightarrow \dfrac{V_1}{V_2}=\dfrac{d_1^2h_1}{\dfrac{1}{4}d_1^22h_1}\\\Rightarrow \dfrac{V_1}{V_2}=\dfrac{1}{\dfrac{1}{2}}\\\Rightarrow \dfrac{V_1}{V_2}=2\\\Rightarrow V_1=2V_2$

El costo del frasco corto por unidad de volumen es

$\dfrac{8000}{V_1}=\dfrac{8000}{2V_2}=\dfrac{4000}{V_2}$

El costo del frasco alto por unidad de volumen es

$\dfrac{4500}{V_2}=\dfrac{4500}{V_2}$

$\dfrac{4000}{V_2}$

Entonces, el costo del frasco corto por unidad de volumen es menor que el costo por unidad de volumen del frasco alto.

Por lo tanto, deberíamos tomar el frasco corto.

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