Solve the inequality. -x/2 is less than or equal to 1. a. x ≤ –2 b. x ≤ 3 c. x ≥ 2 d. x ≥ –2

Mathematics

2 answers:

alexdok [17]3 years ago

8 0

The answer is d. x ≥ –2 .

Vinvika [58]3 years ago

3 0

You have $-\frac{x}{2} \leq 1$ , isolating 'x' we have

 $-\frac{x}{2} \leq 1$
 $-x \leq 2$

Dividing both sides by -1 will flip the sign,
 $x \geq -2$

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A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t = 0 seconds. When the weight it rele

enot [183]

For a better understanding of the explanation provided here kindly go through the file attached.

Since, the weight attached is already at the lowest point at time, t=0, therefore, the equation will have a -9 as it's "amplitude" and it will be a Cosine function. This is because in cosine function, the function has the value of the amplitude at t=0.

Now, we know that the total angle in radians covered by a cosine in a given period is $2\pi$ and the period given in the question is t=3 seconds. Therefore, the angular velocity, $\omega$ of the mentioned system will be:

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

Combining all the above information, we see that the equation which models the distance, d, of the weight from its equilibrium after t seconds will be:

$d=-9cos(\frac{2\pi}{3})t$

Thus, Option B is the correct option. The attached diagram is the graph of the option B and we can see clearly that at t=3, the weight indeed returns to it's original position.