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3 years ago

100 Points!!!

Mathematics

1 answer:

inessss [21]3 years ago

4 0

Answer:

An object moving along the x-axis is said to exhibit simple harmonic motion if its position as a function of time varies as

x(t) = x0 + A cos(ωt + φ).

The object oscillates about the equilibrium position x0. If we choose the origin of our coordinate system such that x0 = 0, then the displacement x from the equilibrium position as a function of time is given by

x(t) = A cos(ωt + φ).

A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction. Simple harmonic motion is repetitive. The period T is the time it takes the object to complete one oscillation and return to the starting position. The angular frequency ω is given by ω = 2π/T. The angular frequency is measured in radians per second. The inverse of the period is the frequency f = 1/T. The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time. It is measured in units of Hertz, (1 Hz = 1/s).

The velocity of the object as a function of time is given by

v(t) = dx(t)/dt = -ω A sin(ωt + φ),

and the acceleration is given by

a(t) = dv(t)/dt = -ω2A cos(ωt + φ) = -ω2x.

You might be interested in

Two fair dice are rolled. Determine whether the events are dependent or independent. (a) (the first die shows 3) and (the two di

Alborosie

Answer: The events are independent

a) p = 1/36 b) p = 5/216

Step-by-step explanation: both events are independent because the fact that the first die shows it sample space {1, 2, 3, 4, 5, 6} does not stop the second die from showing it own sample space too which is {1, 2, 3, 4, 5, 6}.

The sample space of first die = {1, 2, 3, 4, 5, 6}

The sample space of second die = {1, 2, 3, 4, 5, 6}

The sample space of 2 dice rolled at once is seen as attachment to this answer, find attachment below.

Probability that an event will occur = number of time the event will occur / total number of possible outcome of the event

Probability that first die will show 3 = number of times 3 shows up in the event / total number of outcome of the die = P (3)

P (3) = 1/6

Probability that 2 dice sum up to give 7 = 6/ 36 = 1/6 ( from the sample space for 2 dice attached, it is seen that the sum of 7 comes out 6 times and the total sample space is 36)

P (first die show 3) = 1/6

P ( 2 dice sum to 7) = 1/6

P ( first die show 3) and P ( 2 dice sum to 7) = 1/6 * 1/6 = 1/36.

Probability of the first die showing 4 = P(4) = 1/6

Probability of 2 die sum up to give 8 = 5/36

P ( first die show 8) and P ( 2 die sum up to give 8) = 1/6 * 5/36 = 5/216

7 0

3 years ago

Decimal expansion of -11/15

Alenkinab [10]

Don’t listen to the links people -_- they mad annoying

3 0

3 years ago

Perform the following divisions. be sure all answers are reduced to lowest terms. 7/12 ÷ 3/4 =

Free_Kalibri [48]

7/12 / 3/4

You can write it as

7/12 * 4/3

=28/36 = 14/18 = 7/9

So, 7/9 is your answer

7 0

3 years ago

X - 3y +3=0

Arte-miy333 [17]

Answer:

We know that for a line:

y = a*x + b

where a is the slope and b is the y-intercept.

Any line with a slope equal to -(1/a) will be perpendicular to the one above.

So here we start with the line:

3x + 4y + 5 = 0

let's rewrite this as:

4y = -3x - 5

y = -(3/4)*x - (5/4)

So a line perpendicular to this one, has a slope equal to:

- (-4/3) = (4/3)

So the perpendicular line will be something like:

y = (4/3)*x + c

We know that this line passes through the point (a, 3)

this means that, when x = a, y must be equal to 3.

Replacing these in the above line equation, we get:

3 = (4/3)*a + c

c = 3 - (4/3)*a

Then the equation for our line is:

y = (4/3)*x + 3 - (4/3)*a

We can rewrite this as:

y = (4/3)*(x -a) + 3

now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.

We can find this by solving:

(4/3)*(x -a) + 3 = y = -(3/4)*x - (5/4)

(4/3)*(x -a) + 3 = -(3/4)*x - (5/4)

(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)

(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4

(7/12)*x = -(4/13)*a - 17/4

x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7

And the y-value is given by inputin this in any of the two lines, for example with the first one we get:

y = -(3/4)*(- (48/91)*a - 51/7) - (5/4)

= (36/91)*a + (153/28) - 5/4

Then the intersection point is:

( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4)

And we want that the distance between this point, and our original point (3, a) to be equal to 4.

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)^2 + (b - d)^2)

So here, the distance between (a, 3) and ( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4) is 4

4 = √( (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a + (153/28) - 5/4 )^2)

If we square both sides, we get:

4^2 = 16 = (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a - (153/28) + 5/4 )^2)

Now we need to solve this for a.

16 = (a*(1 + 48/91) + 51/7)^2 + ( -(36/91)*a + 3 - 5/4 + (153/28) )^2

16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a - (43/28) )^2

16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 + a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2

16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) + (51/7)^2 + (43/28)^2

At this point we can see that this is really messy, so let's start solving these fractions.

16 = (2.49)*a^2 + a*(23.47) + 55.44

0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16

0 = (2.49)*a^2 + a*(23.47) + 39.44

Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:

$a = \frac{-23.47 \pm \sqrt{23.47^2 - 4*2.49*39.4} }{2*2.49} \\\\a = \frac{-23.47 \pm 12.57 }{4.98}$

Then the two possible values of a are:

a = (-23.47 + 12.57)/4.98 = -2.19

a = (-23.47 - 12.57)/4.98 = -7.23

4 0

3 years ago

Thanh purchased crawfish and shrimp at a local seafood market to use at her restaurant. At the market, crawfish cost $3 per poun

irina1246 [14]

Answer:

22 pounds

Step-by-step explanation:

c+s=52, c = 52-s

3c+5s=200

3(52-s) +5s = 200

156 - 3s +5s = 200

5s-3s = 200-156

2s = 44

Shrimp = 44/2 = 22 pounds

3 0

3 years ago