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2 years ago

1. La Sra. Hamilton quiere comprar pizarras y marcadores para su salón de

1 answer:

7 0

Usando un sistema de ecuaciones, se encuentra que la expresión que muestra la cantidad total que gastará en pizarras y marcadores es:

G = 0.75b + 0.5m.

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¿Qué es un sistema de ecuaciones?

Un sistema de ecuaciones es cuando dos o más variables están relacionadas y las ecuaciones se construyen para encontrar los valores de cada variable.

En este problema, las variables son:

Variable b: Cantidad de tableros.

Variable m: Cantidad de marcadores.

Considerando el precio de cada producto(cada tablero = $0.75, cada marcador = $0.5), la expresión que muestra la cantidad total que gastará en pizarras y marcadores es:

G = 0.75b + 0.5m.

Puede-se aprender más a cerca de sistema de ecuaciones en brainly.com/question/20178040

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$$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}$

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$$= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}$

Using the identity: $(a-b)(a+b)=(a^2-b^2)$

$$= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}$

Denominators are same, you can subtract the fractions.

$$= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}$

Using the identity: $1-\cos ^{2}(x)=\sin ^{2}(x)$

$$= \frac{1+\cos^2 x}{\sin^2x}$

Using the identity: $1=\cos ^{2}(x)+\sin ^{2}(x)$

$$=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}$

$$=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x}$ ------------ (1)

$RHS=2 \cot ^{2} x+1$

Using the identity: $\cot (x)=\frac{\cos (x)}{\sin (x)}$

$$=1+2\left(\frac{\cos x}{\sin x}\right)^{2}$

$$=1+2\frac{\cos^{2} x}{\sin^{2} x}$

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Equation (1) = Equation (2)

LHS = RHS

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Hence proved.

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