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Mekhanik [1.2K]
2 years ago
10

Can someone help me with this please?

Mathematics
1 answer:
photoshop1234 [79]2 years ago
7 0
Your answer is B ...
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HELP PLEASE! :) What is the difference between COMBINING LIKE TERMS and using PROPERTIES OF EXPONENTS?
KiRa [710]

Answer:

Combine terms with the same variable and the same exponent

Step-by-step explanation:

remember that when you combine like terms, you combine the terms with the exact same variable by adding them or subtracting them, depending on the operation they have attached to them. Terms with exponents work exactly the same way! hope this helps you  :)

5 0
3 years ago
Read 2 more answers
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
What is the area of the figure
Free_Kalibri [48]

Answer:

112.5ft^2

Step-by-step explanation:

10 x 9 = 90

9 × 5 × .5 = 22.5

90 + 22.5 = 112.5

8 0
2 years ago
The Reunion Tower in Dallas, Texas, is topped by a spherical dome that has a surface area of approximately 13,924 \pi square fee
Salsk061 [2.6K]

The volume of the spherical dome will be 12.9π cubic feet when the surface area of the dome is 13.924π.

<h3>What is the volume of the sphere?</h3>

The volume of the cone is the amount of quantity, which is obtained in the 3-dimensional space. The dome is the shape of a semi-sphere the volume of the dome will be half of the volume of the sphere.

Given that the Reunion Tower in Dallas, Texas, is topped by a spherical dome that has a surface area of approximately 13,924π square feet.

The volume of the dome will be calculated as below:-

SA = 13.924π

2πr² = 13.92π

r = √6.96

r = 2.63 feet

Volume = 2 / 3 πr³

Volume = ( 2 / 3 ) π ( 2.63)³

Volume = 12.24π cubic feet

Therefore, the volume of the spherical dome will be 12.9π cubic feet.

To know more about volume follow

brainly.com/question/24247548

#SPJ1

7 0
1 year ago
A seamstress needs to cut 15- inches pices of ribbons from a roll of ribbon that is 9 feet in length. What is the greatest numbe
sertanlavr [38]
The seamstress can cut 36, 15-inch pieces of ribbon from 5 rolls of 9 foot long ribbon.
8 0
3 years ago
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