Vector Calculus

A particle of mass m move along the path σ(t)={t^2,sin t, cos t} Calculate the force acting on the particle t=0.

Answers

Answer 1

It seems like σ(t) is the positive function of the particle. Compute its acceleration by differentiating this function twice.

σ(t) = {t ², sin(t ), cos(t )}

σ'(t) = {2t, cos(t ), -sin(t )}

σ''(t) = {2, -sin(t ), -cos(t )}

When t = 0, the acceleration on the particle is

σ'' (0) = {2, -sin(0), -cos(0)} = {2, 0, -1}

Then the force acting on the particle at time t = 0 is

F = {2m, 0, -m}

by Newton's second law.


Related Questions

The cost of a pound of nails increased from ​$2.17 to ​$2.52. What is the percent of increase to the nearest​ whole-number percent?

Answers

Answer:

16%  is the percent of increase to the nearest​ whole-number percent.

Step-by-step explanation:

As the cost of a pound of nails increased from ​$2.17 to ​$2.52.

$2.52 - $2.17 = $0.35

so dividing the 0.35 by 2.17 would give us the percetange of increase

0.35/2.17 = 0.16 which is 16%.

Therefore, 16%  is the percent of increase to the nearest​ whole-number percent.

Latoya finished her English assignment in 1/2 hours. Then she completed her history assignment in 2/3 hours. How much more time did Latoya spend on her history assignment?

Answers

1/6 more hours. Because 1/2 and 2/3 are equal to 3/6 and 4/6. Then you subtract and get 1/6

The time Latoya spend on completing her history assignment is given by the equation A = 1/6 hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The time for Latoya to complete her English assignment = 1/2 hours

The time for Latoya to complete her History assignment = 2/3 hours

So , the difference in time = extra time for Latoya to complete history assignment

Substituting the values in the equation , we get

The difference in time A = ( 2/3 ) - ( 1/2 )

The difference in time A = ( 4 - 3 ) / 6

The difference in time A = 1/6 hours

Hence , the equation is A = 1/6 hours

To learn more about equations click :

https://brainly.com/question/19297665

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Solve these 2 problems please

Answers

Answer:

7 and 10

3 - 7 is -4

1- + 10 is 9

Answer: 8 degrees

Step-by-step explanation:

3-2-1-0-1-2-3-4

Write -0.34 as a fraction in simplest form?

Answers

Answer:

-34/100 is the fraction in simplest form

-17/50 would be the correct simplified answer.

True or False?
To create more batches of a color recipe that will come out to be the same shade of the color, multiply each ingredient by the same number

Answers

Answer:

True

Step-by-step explanation:

Given the following relations on the set of all people. Check ALL correct answers from the following lists: (a) a is older than b A. symmetric B. irreflexive C. reflexive D. antisymmetric E. transitive

Answers

Comlete question is;

Given the following relations on the set of all people. Check ALL correct answers from the following lists:

(a) a is older than b;

A. antisymmetric

B. irreflexive

C. transitive

D. reflexive

E. symmetric

(b) a and b have a common grandparent;

A. reflexive

B. symmetric

C. irreflexive

D. transitive

E. antisymmetric

(c) a has the same first name as b;

A. reflexive

B. irreflexive

C. transitive

D. symmetric

E. antisymmetric

(d) a and b were born on the same day;

A. symmetric

B. reflexive

C. transitive

D. antisymmetric

E. irreflexive

Answer:

a) Options A, B & D.

b) Options C & D.

c) Options C, D & E

d) Options A, B & C

Step-by-step explanation:

a) Options A, B & D.

- It's irreflexive because b is not older than a.

- It's transitive because if a is older than b as we are told and b is older than c, then we can say that a is older than c.

- It's antisymmetric because if a is older than b, then we can say that b is not older than a.

b) Options C & D.

- It's symmetric because if a & b have a common grandparent, then we can say that b and a have a common grandparent.

- It's reflexive because a and b have common grandparents and thus implies all of a's grandparents.

c) Options C, D & E are correct.

It could be Transitive, symmetric or antisymmetric.

d) Options A, B & C are correct.

HELP ME OUT REALLY FAST PLEASEE

Answers

Answer:

1 5/6

Step-by-step explanation:

Answer:

The answer is C

For the suffering you can buy a 6 oz pack of suffering mix for $ $1.98 .The label says a serving size is 1/6 of the Package. If the serving size is 1/6 of the package how many people will 1 package serve?

Answers

Answer:

6... if the serving size is 1/6 of the package, that means it will serve 6 people

Step-by-step explanation:

What is the next number in the sequence? 3, 9, 15, 21, ?

Answers

Answer: 27

Step-by-step explanation:

supposed to ad 6 everytime

Answer:

Your next number would be 27

Step-by-step explanation:

3+6=9

9+6=15

15+6=21

21+6=27

Here is a list of numbers:
0, 10,-18, 7, -14,-7,7,-14,13,0
State the median.

Answers

-21/2 which in decimals would be -10.5. The actual numbers would be -14 and -7 and the median

What is the percent increase when 7200 increases by 1800? 20 percent 25 percent

Answers

Answer:

7200+1800=9000

7200/1800= 72/18= 8/2= 4

100/4 = 25

What is the sequence of 15,12,9,6

Answers

Answer: 3 then 0

Step-by-step explanation:

It’s 3 and then 0 !! :)

The graph represents the cooling curve of ethyl alcohol. Determine the boiling point of ethyl alcohol.
A) 75°C
B) 78°C
C) 80°C
D) 90°C

Answers

Answer:

B

Step-by-step explanation:

what is 1 billion in standard form?​

Answers

Answer:

i think 1,000,000,000

Step-by-step explanation:

1,000,000,000 standard form

Find the slope of the line through the given points.
(8,0) and (10, 10)

Answers

Slope (y2-y1)/(x2-x1)
(10-0)/(10-8) = 10/2 = 5
The slope is 5

Is 18/30 and 3/5 equivalant

Answers

Answer:

yes

Step-by-step explanation:

They both are 0.6 in decimal form

If you can walk 4.9 miles in 2.9 hours, how many minutes does it take to walk 8.73 miles? Round to 1 decimal.

Answers

6.73 I believe.\

Hi HI HI HI HI Hi I HI=

Fact families for 4 3 and 12

Answers

Answer:

i have 5 sisters my dad and mom are still married and im the youngest

Okay so I am confused about a few questions so I'll ask a few.
How do I find the x and y intercepts if they exist, the vertex, and the axis or line of symmetry, and put the function in general form?

f(x) = -2(x + 1)² -4

Answers

the vertex’s coordinates are (-1,4)

Given: M ≅ X
N ≅ Y
YO ≅ NZ
Prove: △MNO ≅ △XYZ

Answers

Answer:

Δ MNO ≅ ΔXYZ ⇒ proved down

Step-by-step explanation:

Cases of congruency

SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ  SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ  ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ  AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ  HL ⇒ hypotenuse and leg of the 1st right Δ ≅ hypotenuse and leg of the 2nd right Δ  

Let us solve the question using the 4th rule above

YZ = YO + OZ

NO = NZ + ZO

∵ OZ = ZO ⇒ from the figure

∵ YO ≅ NZ ⇒ given

YZ NO

In Δs MNO and XYZ

∵ ∠M ≅ ∠X ⇒ given

∵ ∠N ≅ ∠Y ⇒ given

∵ NO ≅ YZ ⇒ proved

→ By using the AAS postulate of congruency.

Δ MNO ≅ ΔXYZ  

What is the solution to this equation?
6x +4= 4x– 2
X=

Answers

Answer:

-3

Step-by-step explanation:

Answer:

I'm not positive but i thank -3

Step-by-step explanation:

I might be rong

A glass is
1
6
full. Then 95cm3 of orange juice is poured in.
The glass is now
4
5
full. What is the total volume of the glass?

Answers

Answer:

let x = the amount of orange juice in a full glass.

the glass is 1/6 full = 1/6 * x

add 95 cubic centimeters and the glass becomes 4/5 full.

equation for that is:

1/6 * x + 95 = 4/5 * x

subtract 1/6 * x from both sides of this equation to get:

95 = 4/5 * x - 1/6 * x

multiply 4/5 * 6/6 and multiply 1/6 * 5/5 and the equation becomes:

95 = 24/30 * x - 5/30 * x

combine like terms to get 95 = 19/30 * x

multiply both sides of the equation by 30/19 to get:

30/19 * 95 = 30/19 * 19/30 * x

simplify to get:

30/19 * 95 = x

solve for x to get x = 150.

the volume of the glass is 150 cubic centimeters.

1/6 * 150 = 25

4/5 * 150 = 120

the difference between 4/5 full and 1/6 full is 95 cubic centimeters.

solution is that the volume of the glass is 150 cubic centimeters.

Step-by-step explanation:

PLEASE HELP
1.6x-(x-2.8)=(0.2x+1.5)-0.7

Solve for x

Answers

The answer is

1.6x-(x-2.8)=(0.2x+1.5)-0.7

1.5-0.7

1.6x-(x-2.8)=0.2x+0.8

1.6x-x

0.6x+2.8=0.2x+0.8

2.8-2.8 0.8-2.8

0.6x=0.2x-2

0.6x-0.2x 0.2x-0.2x

0.4x=-2

0.4x/0.4 -2/0.4

X=-5

$100 if you answer my question

Answers

Answer:

hmm

Step-by-step explanation:

I need help in number 8 ASAP please

Answers

Answer:

it a a and d

Step-by-step explanation:

Find slope plz and ty!!

Answers

Answer:

1/2

Step-by-step explanation:

m=y2-y1/x2-x1

8-6=2

10-6=4

(2/4)/2=(1/2)

hope this helps :3

if it did pls mark brainliest

some one help me with this im lost

Answers

Answer:

We will turn the 1/5 into 1/10, then 1/10 into 2/10 because of the 10%. Then, we will have 8/10 left.

I WILL GIVE BRAINLIEST
Three weeks ago, an art supply store started selling a paint kit for 75% of the original price. Now the kit is 15% off of the sale price. The expression 0.75x - 0.15(0.75x) represents the current price of the paint kit where x is the kit’s original price (in dollars). Find the current price of the kit if it originally cost $48.

Answers

Answer:

$30.60

Step-by-step explanation:

0.75X-0.15(0.75X)

0.75(48)-0.15(0.75(48))

0.75(48)-0.15(36)

36-0.15(36)

36-5.4

30.6

if three people are with 16 sweet how many would 5 be with​

Answers

9.6 but that’s not possible.
hope it helps x

Kevin was having so much fun making cupcakes for his class. He made 2 dozen of them! But there are only 19 kids in his class. Luckily everyone are one cupcake except for Emma. How many cupcakes are left over?​

Answers

6 cupcakes are left 2 dozen is 24 19 kids minus Emma is 18 24-18=6
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