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Arte-miy333 [17]

3 years ago

10

La población de Colombia para el 2018 es de 49 821 512 Si 25'228.444 es la cantidad de mujeres ¿Que porcentaje representan del t

otal de la población?

1 answer:

rusak2 [61]3 years ago

3 0

Answer:

Las mujeres representan el 50.63% de la población.

Step-by-step explanation:

Este problema es un problema de proporciones el cual puede resolverse usando una regla de tres.

El problema nos dice que la población total de Colombia es de 49,821,512 y nos pide calcular qué porcentaje representa el total de mujeres que es igual a 25,228,444. Si llamamos x al porcentaje de mujeres podemos representar esto de la siguiente manera mediante una regla de tres:

Población Porcentaje

49, 821,512 100%

25,228,444 x%

Resolviendo para x tenemos que:

$x=\frac{25,228,444(100)}{49,821,512}=\frac{2,522,844,400}{49,821,512}= 50.6376$

Por lo tanto, las mujeres representan el 50.63% de la población.

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Use Cramer’s rule to solve for x: x + 4y − z = −14 5x + 6y + 3z = 4 −2x + 7y + 2z = −17

V125BC [204]

Looks like the system is

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or in matrix form,

$\mathbf{Ax} = \mathbf b \iff \begin{bmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -14 \\ 4 \\ -17 \end{bmatrix}$

Cramer's rule says that

$x_i = \dfrac{\det \mathbf A_i}{\det \mathbf A}$

where $x_i$ is the solution for i-th variable, and $\mathbf A_i$ is a modified version of $\mathbf A$ with its i-th column replaced by $\mathbf b$ .

We have 4 determinants to compute. I'll show the work for det(A) using a cofactor expansion along the first row.

$\det \mathbf A = \begin{vmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{vmatrix}$

$\det \mathbf A = \begin{vmatrix} 6 & 3 \\ 7 & 2 \end{vmatrix} - 4 \begin{vmatrix} 5 & 3 \\ -2 & 2 \end{vmatrix} - \begin{vmatrix} 5 & 6 \\ -2 & 7 \end{vmatrix}$

$\det \mathbf A = ((6\times2)-(3\times7)) - 4((5\times2)-(3\times(-2)) - ((5\times7)-(6\times(-2)))$

$\det\mathbf A = 12 - 21 - 40 - 24 - 35 - 12 = -120$

The modified matrices and their determinants are

$\mathbf A_1 = \begin{bmatrix} -14 & 4 & -1 \\ 4 & 6 & 3 \\ -17 & 7 & 2\end{bmatrix} \implies \det\mathbf A_1 = -240$

$\mathbf A_2 = \begin{bmatrix} 1 & -14 & -1 \\ 5 & 4 & 3 \\ -2 & -17 & 2 \end{bmatrix} \implies \det\mathbf A_2 = 360$

$\mathbf A_3 = \begin{bmatrix} 1 & 4 & -14 \\ 5 & 6 & 4 \\ -2 & 7 & -17 \end{bmatrix} \implies \det\mathbf A_3 = -480$

Then by Cramer's rule, the solution to the system is

$x = \dfrac{-240}{-120} \implies \boxed{x = 2}$

$y = \dfrac{360}{-120} \implies \boxed{y = -3}$

$z = \dfrac{-480}{-120} \implies \boxed{z = 4}$

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lara [203]

Answer:

<XYZ = 34

Step-by-step explanation:

Remark

Bisected angles means that the original angle (<XYZ in this case) has been cut exactly in half. The two parts that were created from <XYZ are equal so you need only solve for x, solve one of the halves and then double it.

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3x-2x = 2x-2x + 8 Collect like terms on both sides

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