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KiRa [710]
2 years ago
11

Help me with my algebra final exam please.​

Mathematics
2 answers:
kvasek [131]2 years ago
8 0

Answer:

its b

Step-by-step explanation:

zloy xaker [14]2 years ago
3 0
B is the answer because in the photo -1 and then -2 lines up
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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
*<br> E<br> Which angle is an acute angle?
vodomira [7]

Answer:

angle COD is right answer

8 0
3 years ago
Read 2 more answers
You are making fruit baskets using 54 apples, 36 oranges, and 73 bananas. a. Explain why you cannot make identical fruit baskets
GrogVix [38]
Question 1:
73 is a prime number. It can only be divided by 1 and by itself. 

The GCF of the three numbers:
 54                               36                            73
1×54                           1×36                          1×73
2×27                          2×18
3×18                           3×12
6×9                            4×9
                                   6×6

GCF of 54, 36 and 73  is 1

GCF of 54 and 36 is 18

If we divide 54 apples into 18 baskets, we have 3 apples in each basket
If we divide 36 oranges into 18 baskets, we have 2 oranges in each basket
If we divide 73 bananas into 18 baskets, we have 4 bananas in each basket + one banana left over.

So the greatest number of identical fruit baskets we can make with the least amount of fruit left over is 18 baskets
6 0
3 years ago
The area of a cylinder's base is 706.5 square millimeters. The cylinder's lateral area is 471 square millimeters. What is the to
Rzqust [24]
Just add the two bases plus the lateral area. so it would be 706.5+706.5+471.
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3 years ago
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What is the equation of the line written in general form (2,4) (-1,-5)
elena-s [515]
First, you must find the slope, which is -5-4/-1-4, or 1.8, and then put it in point-slope form, or y-4=1.8(x-2), which simplifies to y-4=1.8x-3.6, and so put it in general/standard form, you have to subtract 1.8x from both sides and then add 4 to both sides, and lastly divide both sides of the equation by -1.8 to get x+y=1.889, or x+y=1.6/1.8.   This is not copied and pasted.
6 0
3 years ago
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