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Trava [24]
3 years ago
9

Which of the following number lines represents the solution to x - 5 ≥ -2?

Mathematics
2 answers:
N76 [4]3 years ago
7 0

Step-by-step explanation

Substitute the x for 3

3 - 5 = -2

\geq = greater then or equal to

-2 = -2

The other answer Is incorrect this one is right I did the quiz

mark as brainliest :)

Hunter-Best [27]3 years ago
4 0
This one is your answer hope this helps

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A mass of 1 g is set in motion from its equilibrium position with an initial velocity of 6in/sec, with no damping and a spring c
yan [13]

a) y(t)=0.0016 sin(94.9t) [m]

b) 0.033 s

c) -0.152 m/s

Step-by-step explanation:

a)

The force acting on the mass-spring system is (restoring force)

F=-ky

where

k = 9 is the spring constant

y is the displacement

Also, from Newton's second law of motion, we know that

F=my''

where

m = 1 g = 0.001 kg is the mass

y'' is the acceleration

Combining the two equations,

my''=-ky

This is a second order differential equation; the solution for y(t) is

y(t)=A sin(\omega t-\phi)

where

A is the amplitude of motion

\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{9}{0.001}}=94.9 rad/s is the angular frequency

The spring starts its motion from its equilibrium position, this means that y=0 when t=0; therefore, the phase shift must be

\phi=0

So the displacement is

y(t)=A sin(\omega t)

The velocity of the spring is equal to the derivative of the displacement:

v(t)=y'(t)=\omega A cos(\omega t)

We know that at t = 0, the initial velocity is 6 in/s; since 1 in = 2.54 cm = 0.0254 m,

v_0=6(0.0254)=0.152 m/s

And since at t = 0, cos(\omega t)=1

Then we have:

v_0=\omega A

From which we find the amplitude:

A=\frac{v_0}{\omega}=\frac{0.152}{94.9}=0.0016 m

So the solution for the displacement is

y(t)=0.0016 sin(94.9t) [m]

b)

Here we want to find the time t at which the mass returns to equilibrium, so the time t at which

y=0

This means that

sin(\omega t)=0

We know already that the first time at which this occurs is

t = 0

Which is the beginning of the motion.

The next occurence of y = 0 is instead when

\omega t = \pi

which means:

t=\frac{\pi}{\omega}=\frac{\pi}{94.9}=0.033 s

c)

As said in part a), the velocity of the mass-spring system at time t is given by the derivative of the displacement, so

v(t)=\omega A cos(\omega t)

where we have

\omega=94.9 rad/s is the angular frequency

A=0.0016 m is the amplitude of motion

t is the time

Here we want to find the velocity of the mass when the time is that calculated in part b):

t = 0.033 s

Substituting into the equation, we find:

v(0.033)=(94.9)(0.0016)cos(94.9\cdot 0.033)=-0.152 m/s

4 0
3 years ago
A suit is on sale for $154. If the original price of the suit was $440, what percent was discounted for the sale?
9966 [12]
The dollar amount of the discount is 440 - 154 = $286.
Therefore the percentage discount for the sale is given by:
\frac{286}{440}\times100=65\ percent
3 0
3 years ago
Help please . will give brainliest ​
marishachu [46]

Answer:

A

Step-by-step explanation:

the last number is the y intercept so the intercept in the line is -3.5 so I just matched them up.

3 0
3 years ago
Ram sold a goat for Rs. 4500 at a profit of 20%. what will be the purchased price?
Anna [14]

Answer:

4500x20

Step-by-step explanation:

It will give you your answer

7 0
2 years ago
Find the mean, median, mode, and range of this data: 49, 49, 54, 55, 52, 49, 55. If necessary, round to the nearest tenth.
Darya [45]
Mean: 51.9
Median: 52
Mode: 49
Range: 6
3 0
3 years ago
Read 2 more answers
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