A particle moves so that its position vector with respect to the origin of a reference frame Oxyz is r(t)=bcos w t+bsin w t+vt k,where i,j and k are unit vectors parallel to the co-ordinates axes Ox,Oy and b&V are positive constants.
(i)Find the velocity and speed of the particle
(ii)Describe the path moved by the particle
(iii)Find the acceleration of the particle

Answers

Answer 1

(i) Velocity is the rate of change of position, so if

r(t) = b cos(ω t ) i + b sin(ω t ) j + v t k

then

v(t) = dr/dt

v(t) = -b ω sin(ω t ) i + b ω cos(ω t ) j + v k

The speed of the particle is the magnitude of the velocity, given by

|| v(t) || = √[(-b ω sin(ω t ))² + (b ω cos(ω t ))² + v ²]

… = √[b ²ω ² + v ²]

(ii) The path is a helix. Suppose you zero out the k component. Then the path is a circle of radius b, and the value of ω determines how quickly a particle on the path traverses the circle. Now if you reintroduce the k component, the value of v will determine how far from the plane z = 0 the particle moves in a helical path as t varies.

(iii) Acceleration is the rate of change of velocity, so

a(t) = dv/dt

a(t) = -b ω ² cos(ω t ) i - b ω ² sin(ω t ) j


Related Questions

PLEASE HELP, MATH, PLEASE
Solve for n: n+5/16 = -1​

Answers

[tex]\tt Step-by-step~explanation:[/tex]

To solve for n, we have to isolate n. To do so, we move all the terms that are not n to one side of the equation, and leave n on the other side.

[tex]\tt Steps:[/tex]

Equation: n + 5/16 = -1

Subtract 5/16 on both sides to bring it to the right side of the equation.

[tex]\tt n+5/16-5/16=-1-5/16\\\\n=-\frac{21}{16}~or~-1\frac{5}{16}[/tex]

[tex]\Large\boxed{\tt Our~final~answer:~n=-\frac{21}{16}~or~-1\frac{5}{16} }[/tex]

The weight of an adult beluga whales is known to have a normal distribution with a mean of 1800 pounds in a standard deviation of 300 pound. What is the probability of randomly catching adult beluga whale that weighs between 2000 pounds and 2500 pounds?

Answers

Answer:

.2427

Step-by-step explanation:

If you don't need to show your work:

TI84 calculator:[2nd][vars][normalcdf][lower:2000][upper:2500][μ:1800][σ:300}[enter][enter]

Which of the following is a RATE?


12 to 3


12 stickers to 3 students

Answers

Answer:

gfgfcvfvghcghccghcgcvchdcfgcfcfrtyc

Step-by-step explanation:

–3t — 6t =

syplified ​

Answers

Answer:

-9t

Step-by-step explanation:

-3t -6t

using multiplication of signs

-×-=+

so add the numbers because they have the same

coefficient

-3-6= -9

so

-3t-6t=9t

Please help me ? Please

Answers

Answer:

Step-by-step explanation:

Which tables give sets of values that satisfy the linear function y = 2x – 6

what is (9x+8)^2-54x+48y

Answers

Answer:

81x² + 90x + 48y + 64

Step-by-step explanation:

(9x+8)² = (9x+8)(9x+8) = 9x*9x + 9x*8 + 8*9x + 8*8 = 81x² + 72x + 72x + 64

             = 81x² + 144x + 64

then:

(9x+8)² -54x+48y = (81x² + 144x + 64) -54x + 48y = 81x² + 90x + 48y + 64

if g(x) =x over 2 + 3 find g (4)

Answers

Answer: 2

Step-by-step explanation: 4/2=2

what is the minimum----------------------------------

Answers

Answer: A (-2,5)

Step-by-step explanation:

What is the domain of the relation? ​

Answers

Answer:

I am not certain but it's either the last one or second to last my bet is -4<x<4 but you can try I am not certain tho

3x+4y=2, find 27x•81v

Answers

Ok so when you take 6 from 6 you get 0 so when you get 0 you add 9 so that is your answer 22

A particle moves along a straight line with the equation of motion s = t^{5} - 2 t^{4} Find the value of t (other than 0 ) at which the acceleration is equal to zero.

Answers

Answer:

t = 8/5

Step-by-step explanation:

I'm assuming the equation given is the velocity of the particle

Derive the equation

[tex]5t^4 - 8t^3[/tex]

Set it equal to 0 & solve for t

[tex]0 = 5t^4 - 8t^3\\8t^3 = 5t^4\\8 = 5t\\\frac{8}{5} = t[/tex]

The value of time at which acceleration is zero is required.

The required value of [tex]t=1.2\ \text{s}[/tex]

The function of motion is

[tex]s=(t)^5-2t^4[/tex]

Differentiating with time we get velocity

[tex]s'=5t^4-8t^3[/tex]

Again differentiating with time we get acceleration

[tex]s''=20t^3-24t^2[/tex]

Now acceleration [tex]s''=0[/tex]

[tex]0=20t^3-24t^2\\\Rightarrow 20t^3=24t^2\\\Rightarrow t=\dfrac{24}{20}\\\Rightarrow t=1.2\ \text{s}[/tex]

Learn more:

https://brainly.com/question/10717492

https://brainly.com/question/16053751

can someone tell me the answer please ?

Answers

Answer:

130 degrees

Step-by-step explanation:

Answer:

130 degrees

Step-by-step explanation:

This is a supplementary angle (or whatever the term was for two or more angles that add together to get 180 degrees). There is a total of 7x and 5 degrees. So you would set up the equation 180= 7x+5. Use the properties of equality and subtract 5 from both sides getting 175= 7x. Use the division property of equality to isolate the variable. Divide by 7 to get 25=x. Now just substitute for x in 5x+5 getting 125+5= 130. Sorry if I did a bad job at explaining

Parallel to the line y=-3x + 5 passes through (-4,5)

Answers

Answer:

The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7

Step-by-step explanation:

Given equation of line is:

[tex]y = -3x+5[/tex]

General form of slope-intercept equation of line is:

[tex]y=mx+b[/tex]

Comparing both we get

m = -3

The slope of two parallel line sis equal.

Let m1 be the slope of line parallel to given line, then

m1 = -3

Putting in general form

[tex]y = -3x+b[/tex]

Putting (-4,5) in equation

[tex]5 = -3(-4) +b\\5 = 12+b\\b = 5-12\\b = -7[/tex]

Putting in the general form, we get

[tex]y = -3x-7[/tex]

Hence,

The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7

Can someone help me please

Answers

Answer:

What do you need to know?

Step-by-step explanation:

As I was sitting on a dock, I noticed that the wavelength of the waves were about 6 m long. The crest
of each wave would pass the front of the dock every 8 seconds. Find the frequency of the wave.

Answers

Answer:

IT IS C I BET YOU 6 AND 8

Step-by-step explanation:

The frequency of the wave is equal to: C. 0.125 Hertz

Given the following data:

Wavelength = 6 mTime period = 8 seconds

To determine the frequency of the wave:

A wave can be defined as a disturbance in a medium that progressively transports energy from a source location to another location without the transportation of matter.

Some of the characteristics associated with a wave are:

Speed.Amplitude.Wavelength.Time period.Frequency.

Mathematically, the frequency of a wave is given by the formula:

[tex]Frequency = \frac{1}{Time\;period}[/tex]

Substituting the given parameters into the formula, we have;

[tex]Frequency = \frac{1}{8}[/tex]

Frequency = 0.125 Hertz

Read more: https://brainly.com/question/14708169

Four friends attend a school play and pay $6.75 per ticket. Each also buys a Healthy Snack Bag sold by the Theater Club. If the friends spent a total of $37.00, how much did each Healthy Snack Bag cost, b? Write and solve an equation. (sorry about the wrong grade btw)

Answers

Answer:

$2.5

Step-by-step explanation:

Multiply 4 friends by $6.75 and find the product.

Subtract $27 from $37

Divide 10 by 4

Answer: $2.5

Step-by-step explanation:

Multiply 4 friends by $6.75 and find the product.

Subtract $27 from $37

Divide 10 by 4

Select all that apply.

A graph shows _____ in picture form.


variables
facts
color
statistics
sums
data

Answers

Answer:

Data

Step-by-step explanation:

The answer is data !

Kaylie and Juan are in a Dance-a-thon. Contestants rest for the same amount of time every hour. Kaylie rests for 22 minutes in 4 hours. How long did they rest in 28 hours? Find the unit rate.

Answers

Answer:

154 mins or 2 hour and 34 mins

Step-by-step explanation:

Step 1:

22 : 4          Ratio

Step 2:

22 : 4 = x : 28          Equation

Step 3:

4x = 616       Multiply

Step 4:

x = 616 ÷ 4        Divide

Answer:

x = 154

Hope This Helps :)

An apple tree can grow about 400 apples. Jake says that 13 apple trees can grow about​ 6,000 apples. Do you​ agree? Explain.

Answer: No. Since 13×400=5,200​, 13 apple trees can grow about 5,200 apples.​ Jake's estimate of​ 6,000 is much higher than 5,200.

Answers

Answer:

you answered it

Step-by-step explanation:

you put no blah blah blah

Choose the expanded form of this number.

504,969

Answers

Ummmm
500,000+4,000+900+60+9

Answer:

Step-by-step explanation:

500,000+0+900+60+9

P÷7 when p=42..................

Answers

If p is equal to 42 then you replace the p in the equation. Now it is 42/7. 42/7=6

The answer is 6. Have a nice day/night!!!

Emile is a long-distance runner. He runs at a constant speed of six miles/hour. His goal is to run nine miles on each practice run, but he normally runs a distance that varies three miles more or less than that. Select the correct answer from each drop-down menu. The equation that can be used to find the minimum and maximum time (in hours) Emile runs is_____. For each practice run, the minimum number of hours Emile runs is______ and the maximum number of hours he runs is ______.

Answers

Answer:

[tex]t=\dfrac{9\pm 3}{6}[/tex]

[tex]1\ \text{hour}[/tex]

[tex]2\ \text{hour}[/tex]

Step-by-step explanation:

s = Speed of Emile = 6 miles/hour

d = Distance traveled by Emile = [tex](9\pm 3)\ \text{miles}[/tex]

Time taken to find the minimum and maximum time Emile ran for is

[tex]t=\dfrac{d}{s}\\\Rightarrow t=\dfrac{9\pm 3}{6}[/tex]

The required equation is [tex]t=\dfrac{9\pm 3}{6}[/tex]

The time taken is

[tex]t=\dfrac{9-3}{6}\\\Rightarrow t=\dfrac{6}{6}\\\Rightarrow t=1\ \text{hour}[/tex]

The minimum number of hours Emile runs is 1 hour.

[tex]t=\dfrac{9+3}{6}\\\Rightarrow t=\dfrac{12}{6}\\\Rightarrow t=2\ \text{hour}[/tex]

The maximum number of hours Emile runs is [tex]2\ \text{hour}[/tex].

Answer:

|6x – 9| = 3

1 Hour

2 Hours

Step-by-step explanation:

The equation that can be used to find the minimum and maximum time (in hours) Emile runs is_|6x – 9|= 3_. For each practice run, the minimum number of hours Emile runs is__1 hour_ and the maximum number of hours he runs is _2 hour.

Select all sides lengths x for the missing side of abc

Answers

The answer would be 2

2. The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the rectangle.

Answers

Answer:

The length = x = 15 unitsThe width = x-5 = 10 units

Step-by-step explanation:

Let 'x' be the length of a rectangle

As the width of a rectangle is 5 units less than the length.

so

width of rectangle will be = w = x - 5 units

Area = 150 square units

Using the formula

Area = length × width

[tex]150=\left(x\right)\left(x-5\right)[/tex]

[tex]150=x^2-5x[/tex]

[tex]x^2-5x=150[/tex]

Subtract 50 from both sides

[tex]x^2-5x-150=150-150[/tex]

[tex]x^2-5x-150=0[/tex]

[tex]\left(x+10\right)\left(x-15\right)=0[/tex]

if

[tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]x+10=0\quad \mathrm{or}\quad \:x-15=0[/tex]

[tex]x=-10,\:x=15[/tex]

As length can not be negative. so

x = 15 units

Hence,

The length = x = 15 units

The width = x-5 = 15-5 = 10 units

Carly purchased 9 1/2 pints of ice cream for a party. If each guest will be served exactly 3/5 pints of ice cream, what is the greatest number of guests that Carly can serve?

Answers

Answer:

he can only serve 2

Step-by-step explanation: since  3.5 plus 3.5 is 7.0 if you add one more it turns to 7.0 plus 3.5  10.5 so the greatest he can serve is two people

Alexa and her children went into a movie theater where they sell bags of popcorn for $8 each and pretzels for $5 each. Alexa has $45 to spend and must buy a minimum of 6 bags of popcorn and pretzels altogether. If x represents the number of bags of popcorn purchased and y represents the number of pretzels purchased, write and solve a system of inequalities graphically and determine one possible solution.

Answers

One possible solution from the graph is selling 3 bags of popcorn and 4 bags of pretzel

What is inequality?

Inequality is the non equal comparison of two or more variables and numbers.

Let x represents the number of bags of popcorn purchased and y represents the number of pretzels purchased.

Hence:

8x + 5y ≤ 45   (1)

Also:

x + y > 6   (2)

One possible solution from the graph is (3, 4)

Find out more on inequality at: https://brainly.com/question/24372553

For every 10 students there needs to be 1 chaperone during the trip to the 5 museum. Which of the following ratios does not represent the student to chaperone ratio.


1:10

10 to 1

10:1

10/1

Other: ​

Answers

1:10 does not represent the students to chaperone ratio because for every 10 students, there must be one chaperone.

(a) Solve 5x - 2 = x + 8
Show clear algebraic working.​

Answers

Answer:

Required Answer:-

[tex]{:}\longrightarrow[/tex][tex]\sf 5x-2=x+8 [/tex]

interchange both sides

[tex]{:}\longrightarrow[/tex][tex]\sf 5x-x=8+2 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 4x=10 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {10}{4}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {5}{2}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=2.5 [/tex]

747 is the correct answer

A square lawn has a area 98ft a spin keeper placed at the center of the lawn sprays water in a circular pattern that just covers the lawn what is the radius of the circle

Answers

Answer:

Step-by-step explanation:

Given the area of the square as A = 98ft²

The side length of the square will be equivalent to the diameter of the circle.

First we need to get the length of the square.

Area of a square = L^2

98 = L²

L = √98

L = 9.89 ft

Hence the diameter of the circle is 9.89 ft

radius = diameter/2

radius = 9.89/2

radius ≈ 4.95 feet

Hence the radius of the circle is approximately 4.95 feet

At the end of a snow storm, Mia saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. Let SS represent the depth of snow on Mia's lawn, in inches, tt hours after the snow stopped falling. The table below has select values showing the linear relationship between tt and S.S. Determine the rate at which the snow is melting per hour.

Answers

Answer:

the snow per hour is

Step-by-step explanation:

um wait what chart theres no info to awnser this sorry you may delete this awnser :( but im letting ya know

Answer:

1.5 is the answer.

Step-by-step explanation:

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