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3 years ago

B. Does a12 x a4 = a8 x a8 for all values of a? Explain.

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

3 0

Answer:

We can use the Laws of Exponent to rewrite both sides of the equation:

Let a¹² x a⁴ = a⁸ x a⁸

⇒ a¹²⁺⁴ = a⁸⁺⁸

a¹⁶ = a¹⁶ ✅

⇒ a¹² x a⁴ = a⁸ x a⁸ is true for all values of a.

Explanation:

The equation a¹² x a⁴ = a⁸ x a⁸ is true because, on both the RHS and LHS of the equation, both terms in 'a' have exponents that when added (Law of Multiplication of Exponents) are equal to each other, i.e. 12+4 = 8 + 8.

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2 years ago

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Rina8888 [55]

ANSWER

$x = \frac{\pi}{2} , \frac{7\pi}{6} , \frac{3\pi}{2} , \frac{11\pi}{6}$

EXPLANATION

The given trigonometric equation is

$\cos(x) + 2 \cos(x) \sin(x) = 0$

We factor cos(x) to get:

$\cos(x) (1 + 2 \sin(x) ) = 0$

Apply the zero product property to obtain:

$\cos(x) = 0 \: or \: 1 + 2 \sin(x) = 0$

$\cos(x) = 0 \: or \: \sin(x) = - \frac{1}{2}$

Using the unit circle,

$\cos(x) = 0$

when

$x = \frac{\pi}{2}$

and

$x = \frac{3\pi}{2}$

We know

$\sin(y) = \frac{1}{2}$

when

$y= \frac{\pi}{6}$

The sine function is negative in the third and fourth quadrants.

$x = \pi + \frac{\pi}{6} = \frac{7\pi}{6}$

$x = 2\pi - \frac{\pi}{6} = \frac{11\pi}{6}$

Hence the solutions are:

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