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2 years ago

-6x - 14 < -2 how much is X

Mathematics

1 answer:

IRINA_888 [86]2 years ago

7 0

Add 14 to both sides:
-6x<12
divide by -6 and flip sign because dividing by negative:
x>-2

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A pendulum is set swinging. its first oscillation is through 30 and each succeeding oscillation is through 95% of the angle of t

Marat540 [252]

Answer-

After 76 swings the angle through which it swings less than 1°

Solution-

From the question,

Angle of the first of swing = 30° and then each succeeding oscillation is through 95% of the angle of the one before it.

So the angle of the second swing = $(30\times \frac{95}{100})^{\circ}$

Then the angle of third swing = $(30\times (\frac{95}{100})^2)^{\circ}$

So, this follows a Geometric Progression.

$(30,\ 30\cdot \frac{95}{100},\ 30\cdot (\frac{95}{100})^2............,0)$

a = The initial term = 30

r = Common ratio = $\frac{95}{100}$

As we have to find the number swings when the angle swept by the pendulum is less than 1°.

So we have the nth number is the series as 1, applying the formula

$T_n=ar^{n-1}$

Putting the values,

$\Rightarrow 1=30(\frac{95}{100})^{n-1}$

$\Rightarrow \frac{1}{30} =(\frac{95}{100})^{n-1}$

Taking logarithm of both sides,

$\Rightarrow \log \frac{1}{30} =\log (\frac{95}{100})^{n-1}$

$\Rightarrow \log \frac{1}{30} =(n-1)\log (\frac{95}{100})$

$\Rightarrow -1.5=(n-1)(-0.02)$

$\Rightarrow 1.5=(n-1)(0.02)$

$\Rightarrow n-1=\dfrac{1.5}{0.02}$

$\Rightarrow n-1=75$

$\Rightarrow n=76$

Therefore, after 76 swings the angle through which it swings less than 1°

8 0

3 years ago

Sara goes on a slingshot ride in an amusement park. She is strapped into a spherical ball that has a radius of 3·10^2 centimeter

kondaur [170]

To solve for the volume of a spherical ball, we use the formula,

V = (4πr^3)/3

The given radius of 3x10^2 centimeters converts to 3 meters. Solving for the volume,

V = (4π)x(3^3)/3 = 36π m^3

Thus, Sara is trapped in a spherical ball with a volume of 36π m^3.

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Ostrovityanka [42]

Answer:

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Step-by-step explanation:

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Answer: