2. Solve for x, y, and z

????????????????????

xenn [34]

Answer:

ASA

Step-by-step explanation:

In the 2 triangles

∠J = ∠L

side OJ = side IL

∠O = ∠I

The triangles are congruent by the angle/side/angle (ASA ) postulate

5 0

3 years ago

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

Which expresion shows 18 more than 6 + 18 6 x 18 18 / 6 18 - 6

MissTica

18 more than 6 in a mathematical expression will be 18 + 6 or 6 + 18. Because we are adding 6 to 18 or 18 to 6.

3 0

2 years ago

5*10 divided by 30 -10

sp2606 [1]

The answer to your question would be -25/3

As decimal -8.333333

4 0

2 years ago

What five digit number am i thinking of? It has two prime digits. Digit three is the highest digit. Digit to is the lowest digit

Alexxx [7]

Answer:

47836

Step-by-step explanation:

1. Digit Three is the highest digit which is 8.

2. Digit two is the lowest digit which is 3.

3. Digit five is half of digit three and digit five is 4.

4. Digit one is smaller than digit 3 which is 6 and 8.

5. And we need a prime number for digit 4 which is 7.

Hope this helps.

6 0

3 years ago