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Lubov Fominskaja [6]
3 years ago
9

. Determine whether the vectors (5, −2, 4), (2, −3, 5), and (4, 5−

Mathematics
2 answers:
Tems11 [23]3 years ago
5 0

Answer: The vectors are linearly dependent.

The solution is in the attachment

jekas [21]3 years ago
4 0

Answer:

The vectors are linearly independent

Step-by-step explanation:

These vectors can be written in a matrix form as:

\left[\begin{array}{ccc}5&-2&4\\2&-3&5\\4&5&-7\end{array}\right]

and if the matrix is invertible, the system has a unique solution,  and hence, the vectors that form the matrix are linearly independent.

A matrix is invertible if it's determinant is different from zero.

Suppose A is a matrix, A is invertible if |A| ≠ 0

\left|\begin{array}{ccc}5&-2&4\\2&-3&5\\4&5&-7\end{array}\right| \\

= 5\left|\begin{array}{cc}-3&5\\5&-7\end{array}\right| - (-2)\left|\begin{array}{cc}2&5\\4&-7\end{array}\right| + 4\left|\begin{array}{cc}2&-3\\4&5\end{array}\right|

= = 5[-7(-3) - 5(5)] + 2[2(-7) - 4(5)] + 4[5(2) - 4(-3)]\\= 5(21 - 25) + 2( -14 -20) + 4(10 + 12)\\= 5(-4) + 2(-34) + 4(21)\\= -20 - 68 + 84\\= -4\\

Since this is not zero, we conclude that the vectors are linearly independent.

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The length of the hypotenuse of a right triangle is 24. If the length of one leg is 8, what is approximate length of the other l
Verdich [7]

Something that a right triangle is characterised by is the fact that we may use Pythagoras' theorem to find the length of any one of its sides, given that we know the length of the other two sides. Here, we know the length of the hypotenuse and one other side, therefor we can easily use the theorem to solve for the remaining side.

Now, Pythagoras' Theorem is defined as follows:

c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Given that we know that c = 24 and a = 8, we can find b by substituting c and a into the formula we defined above:

c^2 = a^2 + b^2

24^2 = 8^2 + b^2 (Substitute c = 24 and a = 8)

b^2 = 24^2 - 8^2 (Subtract 8^2 from both sides)

b = √(24^2 - 8^2) (Take the square root of both sides)

b = √512 (Evaluate 24^2 - 8^2)

b = 16√2 (Simplify √512)

= 22.627 (to three decimal places)

I wasn't sure about whether by 'approximate length' you meant for the length to be rounded to a certain number of decimal places or whether you were meant to do more of an estimate based on your knowledge of surds and powers. If you need any more clarification however don't hesitate to comment below.

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3 years ago
When I solve this problem I get a big number, and I don't kwow if it's Ok:
Jlenok [28]

Answer:

undefined

Step-by-step explanation:

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3 years ago
What is the length of the hypotenuse of the triangle?
masha68 [24]
10 star-root 2 end units
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Imaginá que tenés 125 dados cúbicos del mismo tamaño ¿Cuantos dados de altura tiene el cubo de mayor tamaño que podés armar apil
kumpel [21]

Answer:

(i) Debemos apilar 5 dados para construir el cubo de mayor tamaño.

(ii) Se necesita 121 dados cuadrados para formar el cuadrado con la mayor cantidad de dados posibles, quedando 4 dados sobrantes.

Step-by-step explanation:

(i) Sabemos por la Geometría Euclídea del Espacio que un cubo es un sólido regular con 6 caras cuadradas y longitudes iguales. Cada dado tiene un volumen de 1 dado cúbico y 125 dados dan un volumen total de 125 dados cúbicos.

El volumen de un cubo está dado por la siguiente fórmula:

V = L^{3}

Donde:

L - Longitud de la arista, medida en dados.

V - Volumen del cubo, medido en dados cúbicos.

Ahora, necesitamos despejar la longitud de la arista para calcular la altura máxima posible:

L = \sqrt[3]{V}

Dado que V = 125\,dados^{3}, encontramos que la altura del cubo de mayor tamaño sería:

L =\sqrt[3]{125\,dados^{3}}

L = 5\,dados

Debemos apilar 5 dados para construir el cubo de mayor tamaño.

(ii) El área cuadrada formada por cubos está determinada por la siguiente fórmula:

A = L^{2}

Donde:

L - Longitud de arista, medida en dados.

A - Área, medida en dados cuadrados.

Puesto que la longitud de arista se basa en un conjunto discreto, esto es, el número de dados disponibles, debemos encontrar el valor máximo de L tal que no supere 125 y de un área entera. Es decir:

L \leq 125\,dados

Si cada cubo tiene un área de 1 dado cuadrado, entonces un cuadrado conformado por 125 dados tiene un área total de 125 dados cuadrados. Entonces:

L^{2}< 125\,dados^{2}

Esto nos lleva a decir que:

L < 11.180\,dados

Entonces, la longitud máxima del cuadrado con la mayor cantidad de cubos posible es de 11 dados. El número total requerido de cubos es el cuadrado de esa cifra, es decir:

n = (11\,dados)^{2}

n = 121\,dados

Se necesita 121 dados cuadrados para formar el cuadrado con la mayor cantidad de dados posibles, quedando 4 dados sobrantes.

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Which rational number equals 0.333...? 1 over 5, 1 over 3, 3 over 10, 3 over 5
lana [24]

Answer:

1/3

Step-by-step explanation:

let x=0.333...

10x=3.333...

subtract

9x=3

x=3/9=1/3

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3 years ago
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