The position of a particle is given by the expression x = 6.00 cos (2.00πt + 2π/5), where x is in meters and t is in seconds. (a) Determine the frequency. (Hz) (b) Determine period of the motion. (s) (c) Determine the amplitude of the motion. (m) (d) Determine the phase constant. (rad) (e) Determine the position of the particle at t = 0.350 ( s. m)

Answers

Answer 1

The position of the particle at t = 0.350 s is approximately -3.94 m.

(a) The expression for the position of the particle is x = 6.00 cos (2.00πt + 2π/5), where t is in seconds. The coefficient of t in the argument of the cosine function is 2πf, where f is the frequency in hertz. Therefore, we have:

2πf = 2.00π

f = 1.00 Hz

Thus, the frequency of the motion is 1.00 Hz.

(b) The period of the motion is the time required for one complete cycle of the motion. The period is given by:

T = 1/f

T = 1/1.00

T = 1.00 s

Thus, the period of the motion is 1.00 s.

(c) The amplitude of the motion is the maximum displacement of the particle from its equilibrium position. In this case, the amplitude is 6.00 m, since the coefficient of the cosine function is 6.00.

Thus, the amplitude of the motion is 6.00 m.

(d) The phase constant is the constant term in the argument of the cosine function. In this case, the phase constant is 2π/5, since this is the constant term in the expression for x.

Thus, the phase constant is 2π/5 radians.

(e) To determine the position of the particle at t = 0.350 s, we substitute t = 0.350 s into the expression for x:

x = 6.00 cos (2.00π(0.350) + 2π/5)

x = 6.00 cos (0.700π + 2π/5)

x = 6.00 cos (9π/10)

x ≈ -3.94 m

Thus, the position of the particle at t = 0.350 s is approximately -3.94 m.

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Related Questions

Please help am stuck thanks

Answers

Answer:

12.4 did this before

Step-by-step explanation:

Answer:

sɪʀ ʏᴏᴜʀ ᴀɴsᴡᴇʀ ɪs 12.4

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴍɪᴅ ᴘᴏɪɴᴛ ᴛʜᴇʀᴏᴇᴍ

Write an recursive formula for an, the nth term of the sequence 7, 10, 13,

Answers

Answer:

What's the nth term for 7,10,13,16? The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.

Step-by-step explanation:

Convert equation from slope intercept form to standard form y=-7/3x+1

Answers

Answer:

7x + 3y = 3

7x + 3y = 3

7x + 3y = 3

what are the answers to the variables? and how do i find them?

Answers

Answer:

Step-by-step explanation:

A man shares a $1,200,00 inheritance between his 3 sons in ratio 1: 3: 6. Calculate the difference between the largest share and the smallest share

Answers

Answer:

60000

Step-by-step explanation:

You should treat the first son with the 1 ratio as x. Because of this, the second son would be 3x and the third would be 6x. All of them need to equal 120000 so 10x=120000. Next you isolate the and x= 12000. Fill in 1200 for x and the first son gets 12000, the second gets 36000, and the third gets 72000. Lastly you subtract and you get 60000.

Find the unknown side length x. Write your answer in simplest radical form

Answers

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 30² = 50²

x² + 900 = 2500 ( subtract 900 from both sides )

x² = 1600 ( take the square root of both sides )

x = [tex]\sqrt{1600}[/tex] = 40 → B

Do the following dogs appear to be SIMILAR? Please answer Yes or No and explain using math terminology!

Answers

Answer:

yes but no

Step-by-step explanation:

one is bigger than the other by prolly 1 foot

Answer:

1 is bigger by abt a foot or so

Step-by-step explanation:

solve for x or find x​

Answers

Answer:

63+ 2x- 17 = 180 degree

or, 2x+46=180degree

or, 2x=180-46=134degree

or, x = 134÷2=67 degree ans.

Find the coordinates of the turning point when y=5x^3 - 6x^2 - 4X + 8

Answers

Given:

The equation is

[tex]y=5x^3-6x^2-4x+8[/tex]

To find:

The coordinates of the turning point.

Solution:

We have,

[tex]y=5x^3-6x^2-4x+8[/tex]

Differentiate with respect to x.

[tex]\dfrac{dy}{dx}=5(3x^2)-6(2x)-4(1)+(0)[/tex]

[tex]\dfrac{dy}{dx}=15x^2-12x-4[/tex]

For the turning points [tex]\dfrac{dy}{dx}=0[/tex].

[tex]15x^2-12x-4=0[/tex]

Using quadratic formula:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{-(-12)\pm \sqrt{(-12)^2-4(15)(-4)}}{2(15)}[/tex]

[tex]x=\dfrac{12\pm \sqrt{144+240}}{30}[/tex]

[tex]x=\dfrac{12\pm \sqrt{384}}{30}[/tex]

Now,

[tex]x=\dfrac{12+\sqrt{384}}{30}\text{ and }x=\dfrac{12-\sqrt{384}}{30}[/tex]

[tex]x\approx 1.053\text{ and }x\approx-0.253[/tex]

Putting x=1.053 in the given equation, we get

[tex]y=5(1.053)^3-6(1.053)^2-4(1.053)+8[/tex]

[tex]y\approx 2.973[/tex]

Putting x=−0.253 in the given equation, we get

[tex]y=5(-0.253)^3-6(-0.253)^2-4(-0.253)+8[/tex]

[tex]y\approx 8.547[/tex]

Therefore, the turning points are (1.053,2.973) and (-0.253, 8.547).

someone plz help!!!!

Answers

Answer:

7/8 > 3/4

Step-by-step explanation:

Find a common denominator first and here it is 8. To get 3/4 to 8ths, you multiply the numerator and denominator by 2 to get 6/8 and 7/8 is greater

Mr. Velasquez built a playground. It has one section with a slide and another section with a swing set. A pathway connects the two areas. The slide is 2 meters high. The ares and the pathway are covered in asphalt. Mr velasquez want to know how much of the playground is covered in asphalt

Answers

Answer:

[tex]A_1 = 24m^2[/tex] -- Swing set

[tex]A_2 = 16m^2[/tex] -- Slide

[tex]A_3 = 5m^2[/tex] --- Pathway

Step-by-step explanation:

Missing part of the question:

Fill in the table above to show the area of each section (see attachment for table)

The area of each section is calculated as:

[tex]Area = Length * Width[/tex]

For the Swing set

[tex]A_1 = 8m * 3m[/tex]

[tex]A_1 = 24m^2[/tex]

For the Slide

[tex]A_2 = 8m * 2m[/tex]

[tex]A_2 = 16m^2[/tex]

For the Pathway

[tex]A_3 = 5m * 1m[/tex]

[tex]A_3 = 5m^2[/tex]

The total area is:

[tex]Area=A_1 + A_2 + A_3[/tex]

[tex]Area = 24m^2 + 16m^2 + 5m^2[/tex]

[tex]Area = 45m^2[/tex]

What percent of 56 is 42?
I need an answer ASAP
a
23%
b
42%
c
75%
d
90%

Answers

Answer:

nicki monaj is the queen of rap

Step-by-step explanation:

periodt purr

The answer is C. 75%!

a cyclist travels for 5 days and covers 375km in total.
He covers 67km 78km 46km and 89km on the fist 4 days .How far does he travel on day 5 ​

Answers

Answer:

95km

Step-by-step explanation:

5 days = 375km

4 days = 67km + 78km + 46km + 89km= 280km

5 days - 4days = the 5th day

375km - 280km = 95km

Can someone help me with number 3 please there is 3 answers!!

Answers

Answer:

m<J = 83

m<L = 97

m<M = 97

Step-by-step explanation:

The corners across (left to right/right to left) from each other of a trapezoid are always equal.

So, it would be like this:

Angle J is equal to angle K

Angle M is equal to angle L

See how they are across from each other?

Therefore, Angle J will be 83 degrees.

To find the other 2 angles subtract 83 from 180

180 - 83 = 97

So, Angle L and M are 97 degrees.

To check your answer you can add up all the corners and they should equal 360 degrees:

83 + 83 + 97 + 97 = 360

360 = 360

Hope this helps!!

- Kay :)

BEN ELİF81 BU HESABI TAKİP EDERMİSİN EĞER BENİ TAKİP EDERSENİZ BEN DE SİZİ TAKİP EDERİM.
SİZE GÜVENİYORUM:)​

Answers

256363 okay i don’t know just try okay

HELLLPPPPP WITHHHH MATHHHH

Answers

Answer:

54 inches

Step-by-step explanation:

6/18=7/x

6x=7(18)

6x=126

x=21

21+15=18=54

How many terms are in this expression?
s+3u+10=

Answers

There are 3 terms in this expression s, 3u, and 10

12.) Joe sold 56 tickets to the school play and collected $215. Tickets
for adults cost $4.50 and student tickets cost $3.50 each. How many
of each did he sell?

Answers

Answer:

I DONT KNOW!!

Step-by-step explanation:

Anits takes 8 hours to build 5 birdhouses. How many birdhouses could she Build in 24 hours?

Answers

The answer would be 15 because the problem states that it takes 8 hours to build 5 birdhouses and they want to know how many she can build in 24 hours if you multiply 8 and 5 with the number 3 you would get 24 hours and 15 birdhouses.

Mr. Villa bought 91.25 inches of plastic
labeling tape. He will make labels 1.25 inches long
each. How many labels can he make?
1. What is asked in the problem?
A. the measurement of the tape
B. the labels can he make to the tape
C. inches of plastic labeling tape
D. Mr. Villas tape
2. What is the answer?
A. he can make 69 labels
B. he can make 70 labels
C. he can make 72 labels
D. he can make 73 labels​

Answers

Answer:

1) B. the labels can he make to the tape

2) D. he can make 73 labels

Step-by-step explanation:

1) We are told that He will make labels 1.25 inches long each. We are asked the number of labels he can make.

Thus, correct answer is option B.

2) He wants to make labels 1.25 inches long out of 91.25 inches of plastic.

Thus, number of labels he can make = 91.25/1.25 = 73 labels

rs10,000 for 1 year at 8% per annum compounded half yearly.​

Answers

Step-by-step explanation:

Answered 1 year, 9 months ago

Given,

Principal, P =Rs.10000,  Rate, R = 8% per annum compounded half yearly for 1 year. 

Now, There are two half years in a year. Therefore compounding has to be 2 times. 

And rate = half of 10% = 5% half yearly.

Therefore, the required amount =   = Rs. 10816

And Compound Interest, C.I. = Amount - Principal = Rs. (10816 - 10000) = Rs. 816.

hope it helps you

eddie who earns $5 per hour worked two hours longer zach who earns $12 per hour. together they earn $30

Answers

5(h+2)+12(h)=30
h=20/17

Can anyone help me with this problem # 9

Answers

Answer:

72 apples will be used and 4 will not

Answer:

She will use 72 apples and 4 apples will not be used.

Step-by-step explanation:

If she requires 9 apples for one pie... the she can make only 8 pies out of 76 apples.

hence she uses 72 apples...

pleaseee help me asap
1.What is the unit rate of the graph?

2.What is the slope of the graph?

Compare your answers to #1 and #2

Answers

Answer:

The unit rate[tex]\frac{4}{1}[/tex] of the graph is 4, the slope of the graph is 4, and the comparison between answers is that they are equal.

Step-by-step explanation:

For every increase of 1 in the X value of the graph, the Y value increases by 4, so the slope would be [tex]\frac{4}{1}[/tex] or 4.

Plz help due tomorrow

Answers

Answer:

 It's C) -6y

Step-by-step explanation:

I know someone already answered but I figured I could explain since it looks like you are getting a little confused. The reason it's not A is because its

-5 + 5 which is zero. So it gets rid of x so your just left with -6y. If it was

5x+5x then it would 10x but the negative makes it 0

An icecream factory makes 140 quarts in 10 hours . How much can be made in 12 ? ​

Answers

Find quarts per hour:

140 quarts / 10 hours = 14 quarts per hour.

Now multiply quarts per hour by hours:

14 quarts per hour x 12 hours = 168 quarts

What is the area, in square inches, of the trapezoid below? 15.7 in 8 in 6.6 in​

Answers

Answer:

What is the area, in square inches, of the trapezoid below? 15.7 in 8 in 6.6 in​-by-step explanation:

The area, in square inches, of the trapezoid, is 89.2 in².

We have given that,

A = 89.2 in²

The area (A) of a trapezoid is calculated as,

What is the area trapezoid?

A = 1/2 h (b₁ + b₂ )

where h is the perpendicular height and b₁, b₂ the parallel bases

Here h = 8, b₁ = 6.6, b₂ = 15.7 , then

A = 1/2 × 8 × (6.6 + 15.7)

A= 4 × 22.3

A= 89.2 in²

The area, in square inches, of the trapezoid, is 89.2 in².

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Sofia is making a batch of slime using a recipe that includes glue, water, and salt solution. She uses 7.5 fl. oz of glue. The amount of glue is 12.5 times the amount of salt solution. There are 4.2 less fluid oz of salt solution in the water. How many fluid ounces of water does Sofia use to make a batch of slime?

Answers

Answer:

its 4.8

Step-by-step explanation:

i divided 7.5 by 12.5 and got 0.6 and added 4.2 and got 4.8

Equation is formed of two expressions. The amount of water that is used by Sofia to make the slime is 4.8 fl oz.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the amount of salt solution used by Sofia be x, and the amount of water used by Sofia be y.

As it is given that the amount of glue used is 12.5 times the amount of salt solution used, and the amount of glue used is 7.5 fl oz. Therefore, the equation can be written as,

Amount of glue = 12.5 x Amount of salt solution

[tex]7.5 = 12.5 \times x\\\\x = \dfrac{7.5}{12.5}\\\\x = 0.6[/tex]

Also, it is given that the amount of water used is 4.2 fl oz. less than the amount of salt solution used, since we know the amount of salt solution used, therefore, the equation can be written as,

Amount of salt solution = Amount of water - 4.2 oz

[tex]x = y -4.2\\\\(0.6)=y-4.2\\\\y = 4.8[/tex]

Hence, the amount of water that is used by Sofia to make the slime is 4.8 fl oz.

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The question is 3(2x +4) = 6x + 10

Answers

Answer:

no solution

Step-by-step explanation:

when you distribute, the 6x on each side cancel out leaving there to be no solution to the problem. I attached a photo of my work as well.

Answer:

The answer is False meaning it's no solution

Step-by-step explanation:

1. Distribute 3 through the parentheses which will be 6x+12=6x+10

2.Cancel equal terms on both sides of the equation and you will get 12=10 which isn't a true statement.

If 3x−y=12, what is the value of
8x
2y

Answers

Answer:

[tex]8x=32\\2y=-24[/tex]

Step-by-step explanation:

When solving for 1 variable, set the other to 0 and solve.

[tex]3x-y(0)=12\\3x=12\\x=4\\4*8=32\\8x=32\\\\3(0)-y=12\\-y=12\\y=-12\\-12*2=-24\\2y=-24[/tex]

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