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Oliga [24]
3 years ago
10

What is the volume of the figure down below?

Mathematics
1 answer:
11111nata11111 [884]3 years ago
6 0
The answer is C. All calculations of a cone or the cone equal up to 353.77. 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
2.) Two students are working on a simplification problem. Their work is shown below. Is either of
kvasek [131]

Answer:

Both Jeff and Lori are wrong.

Step-by-step explanation:

3 -  \frac{(4 \times 3)^{2} }{2}  + (1 \times 6)

3 - \frac{12^{2}}{2}  + 6

3 -  \frac{144}{2}  + 6

3 - 72 + 6

- 72 + 9

- 63

-63 is the final answer

8 0
3 years ago
HI HI HI NEED ANSWER QUICK PLZ THXXX
g100num [7]

Answer:

Cement

Step-by-step explanation:

You need answer quick, I'm not explaining.

5 0
2 years ago
Read 2 more answers
Find X, last two anwsers are 4 and 8
IgorLugansk [536]

Answer:

9

Step-by-step explanation:

8X+4=360-108-80-96

8X+4=76

8X=76-4

8X=72

X=72/8

X=9

8 0
3 years ago
Find the slope of the line through the given points.<br> (10, 11) and (15, 16)
Fudgin [204]

Answer:

Step-by-step explanation:

-5/-5

7 0
3 years ago
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