Two particles have positions at time t given by s1=4t-t^2 and s2=5t^2-t^3. Find the velocities

Answers

Answer 1

Step-by-step explanation:

Given that,

The positions of the first particle,[tex]s_1=4t-t^2[/tex]

Velocity,

[tex]v_1=\dfrac{ds_1}{dt}\\\\v_1=\dfrac{d(4t-t^2)}{dt}\\\\v_1=4-2t[/tex]

Position,

[tex]s_2=5t^2-t^3[/tex]

[tex]v_2=\dfrac{ds_2}{dt}\\\\v_2=\dfrac{d(5t^2-t^3)}{dt}\\\\v_2=10t-3t^2[/tex]

Hence, this is the required solution.


Related Questions

Help please
If the measure of angle 6 is 140 degrees and the measure of angle 7 is (x + 30) degrees, what value of x will guarantee n ∥ m?

Answers

Answer:

x = 10

Step-by-step explanation:

If n // m , then angle 6  and angle 7 are co interior angles and they are supplementary.

∠6 + ∠7 = 180

140 + x +30 = 180

       x + 170 = 180

               x = 180 - 170

x = 10

what s the equation of the line through the origin and (-2, 3)

Answers

Answer:

y=[tex]\frac{-3x}{2}[/tex]

Step-by-step explanation:

Hi there!

We need to find the equation of the line that passes through the origin (the point (0,0)) and (-2,3)

There are 3 ways to write the equation of the line, although the most common way is slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

So we need to find the slope of the line first

The formula for the slope (m) calculated from two points [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are points

We have the needed information to calculate the slope, but let's label the values of the points to avoid any confusion

[tex]x_{1}[/tex]=0

[tex]y_{1}[/tex]=0

[tex]x_{2}[/tex]=-2

[tex]y_{2}[/tex]=3

Now substitute their values into the equation and find m

m=[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

m=[tex]\frac{3-0}{-2-0}[/tex]

subtract

m=[tex]\frac{3}{-2}[/tex]

so the slope of the line is [tex]\frac{3}{-2}[/tex]. It can also be rewritten as [tex]\frac{-3}{2}[/tex]

Here is the equation of the line so far:

y=[tex]\frac{-3x}{2}[/tex]+b

we need to find b

As the equation passes through both (0,0) and (-2,3), we can use either one of them to solve for b

Let's take (0,0) for this case

Substitute 0 as x and 0 as y

0=-[tex]\frac{3}{2}[/tex](0)+b

multiply

0=0+b

add 0 to both sides

0=b

So b is 0

The equation of the line therefore is y=[tex]\frac{-3x}{2}[/tex]

Hope this helps!

If y is proportional to x, find the missing number.

A. 15
B. 12
C. 16
D. 18

HELPPP!!!!

Answers

Answer:

C. 16

Step-by-step explanation:

5 is half of 10, so 8 should be half of the next number.

Answer:

C. 16

Step-by-step explanation:

[tex] \frac{y}{x} = \frac{10}{5} = \frac{?}{8} \\ \frac{2}{1} = \frac{?}{8} [/tex]

cross multiplying

[tex]16 = ?[/tex]

so the missing number is 16

How do I solve for X HELP

Answers

Answer:

x = 4 degrees

Step-by-step explanation:

The two angles have the same measurement. They are opposite angles.

26x + 7 = 31x - 13

Group like terms:

26x - 31x = -13 - 7

-5x = -20

x = 4

Check if you want to make sure.

Step-by-step explanation:

[tex]here \: is \: your \: solution : - \\ \\ both \: angles \: are \: equal \: (vertical \: anges) \\ \\ 26x + 7 = 31x - 13 \\ \\ solving \: the \: equation \: \\ \\ 26x - 31x = - 13 - 7 \\ \\ - 5x = 20 \\ \\ x = -20 \div 5 \\ \\ x = \: 4 \: degrees \: \: \: \:(Answer ✓✓✓( \\ \\ \huge\mathcal\blue{happy \: life (. ❛ ᴗ ❛.) }[/tex]

3
49:51
What is the solution to the system that is created by the equation Y =-X+6 and the graph shown below?
10
8
6
4
-10-8-6-44
2
4 6
8 10 x
4
46
-8
10
O (-8,-4)
O (-4,-2)
(4.2)
(6.3)
Mark this and retum
Save and Exit
Next
Submit

Answers

If you draw the graph of y = -x + 6 on the above graph the solution to system will be the coordinates of the point of intersection.
the equation of the line drawn above is y = 0.5x

so you can also find the solution by solving the system
y = 0.5x
y = -x + 6

0.5x = -x + 6
1.5x = 6
x = 6/1.5 = 4

and y = 0.5*4 = 2

The answer is (4, 2) - the third choice.

PLEASE HELP NEED HELP W ALGEBRA 2 QUESTION!!

the graph of f(x) = 3 sqr root x+8 is shown which statement is true

1. The function is only increasing x > -8
2. The function is only increasing when x > 0
3. The function is always decreasing
4. The function is always increasing

Pls say what number choice in your answer! Thanks!

Answers

Answer:

2. increasing when x > 0

the result of root is a positive number

and since there is no value of neg number in roots so it's increasing when x>0

plus in zero it self has a positive number (0,8)

but u cannot find either it's increasing or decreasing in zero bcoz in first derivative test

when x =0

y= not defined

Find the perimeter of ΔNOP. Round your answer to nearest tenth if necessary. Figures are not necessarily drawn to scale

Answers

Answer:

P = 157.5 units

Step-by-step explanation:

Find x if : (-3/7)^-19 ÷ (-3/7)^8 = (-3/7)^- 2x+1​

Answers

Answer:

x=14

Step-by-step explanation:

(-3/7) power (-19-8)= (-3/7) power -2x+1

-19-8= -2x+1

-27= -2x+1

-27-1= -2x

-28= -2x

x=28/2

x=14

A 4-column table with 4 rows. Column 1 is labeled number of friends with entries 3, 5, 7, 9. Column 2 is labeled Carnival Cost with entries 51.5, 75.5, 99.5, 123.5. Column 3 is labeled Aquarium Cost with entries 43.5, 72.5, 101.5, 130.5. Column 4 is labeled Wave Pool Cost with entries 50.25, 61.25, 85.75, 110.25.
Gale wants to compare the cost of the events.

Aquarium: $14.50 each ticket

Carnival: c = 15.5 + 12f

Wave pool: $16.75 each, but $12.25 each for groups larger than 4

Which of the claims Gale makes is true?
The table represents all possibilities.
The carnival always costs the least.
The Aquarium always costs the most.
(7, 101.5) is an ordered pair used to represent the aquarium cost.

Answers

Answer:

D.(7, 101.5) is an ordered pair used to represent the aquarium cost.

Hope it helps :)

Step-by-step explanation:

Answer: it is d - (7, 101.5) is an ordered pair used to represent the aquarium cost

Step-by-step explanation: got it right on edge 2022

Hello can someone help me with this problem

Answers

no lol do it yourself

Write the product as a single power. 6^(5) * 6^(2) * 6^(5)

Answers

Answer:

6^12

Step-by-step explanation:

add up all the exponents

[tex]\displaystyle\bf \boxed{a^m\cdot a^n=a^{m+n}}\\\\6^5\cdot 6^2\cdot6^5=6^{5+2+5}=\boxed{6^{12} }[/tex]

PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS ANSWERRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR

Answers

Answer:

ssssssssssssssssssssssssssssssssssssssssssssssss

Answer:

¼. 1000

Step-by-step explanation:

25% = 25/100

= 1/4

Therefore,

25% of 1,000 is the same as

1/4. 1000

find the next four terms of the sequence 5, 4, 9, 13, 22

Answers

Answer:

38

Step-by-step explanation:

The first term of the given sequence is 9.

The second term is 13

= 9 + 4 . = 9 + 2 × 2.

The next number is 22.

= 13 + 9 . = 13 + 3 × 3 .

In the same way the next number of the given sequence will be

22 + 4 × 4 .

= 22 + 16 = 38.

Which equation in slope-intercept form represents a line that is parallel to y=-4x-5 and passes through the points (0,0)?

Answers

Answer:

y = 0x

Step-by-step explanation:

y=-4x-b

0 = -4(0) + b

0 = 0 + b

0

A company uses two vans to transport
workers from a free parking lot to the
workplace between 7:00 and 9:00 a.m.
One van has 6 more seats than the other.
The smaller van makes two trips every
morning while the larger one makes only
one trip. The two vans can transport 57
people, maximum.
How many seats does the larger van have?

Answers

x is the seats in the small van.

y is the seats in the large van = (x + 6). Since the large has 6 more seats.

Since the 2 vans can transport 57 people.

Small van makes 2 trips = 2x.

Large van makes one trip = (x + 6).

2x + (x +6) = 57

2x + x + 6 = 57

3x + 6 = 57

3x = 57 -6

3x = 51

x = 51/3

x = 17.

The larger van has (x + 6) = (17 + 6) = 23.

The larger van has 23 seats.

Answer:

The larger van has 23 seats

Step-by-step explanation:

Create a system of Equations:

1. Define variables.

> let x=small van and y=larger van

2. create 2 equations based on the information given.

> y = 6 + x

> 2x + y = 57

3. Use any method to solve

Substitution: 2x + (6 + x) = 57. x=17

                      now plug x in to the original equation to solve for y (the larger van)

                      y = 6 + 17 and y = 23

Elimination: 2y = 12 + 2x

                     y = 57 - 2x

         3y = 69  and y = 23


PLEASE HELP.
if v1….

Answers

I believe the answer is 4.4

What is the largest prime number less than 200?

Answers

Answer:

199

Step-by-step explanation:

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.

A prime number is a number that has only two divisors: 1 and itself.

Exaples:

2, 3, 5, 7, 11, 13, 17, 19, 23 ...

We know: all primes except 2 are odd.

Let's check the number 199:

We know:

13² = 13 · 13 = 169 < 200

17² = 17 · 17 = 289 > 200

199 : 3 is not an integer

199 : 5 is not an integer

199 : 7 is not an integer

199 : 11 is not an integer

199 : 13 is not an integer

199 : 17 is not an integer

Therefore 199 is thelargest prime number less than 200.

Drag the tiles to the correct location on the image.Not all tiles will be used.​

Answers

Answer:

Given,

side=4√5 millimetres

=4×4√5

=16√5

Perimeter= 16√5 milimetre

Area= side× side

=4√5 × 4√5

=80

Area= 80 square milimeters

------------------------------

hope it helps...

have a great day!

Answer:

solution:-

Given,

side=4√5 mm

=4×4√5

=16√5

Perimeter= 16√5 mm

Area= side× side

=4√5 × 4√5

=80

Area= 80 square milimeters

------------------------------

hope it is helpful to you

stay safe healthy and happy

can anyone answer this? (2y²-3xy)÷y.​

Answers

the answer would be y x(2y-3x)

Answer:

2y - 3x

Step-by-step explanation:

Given

(2y² - 3xy) ÷ y

Divide each term on the numerator by y , that is

[tex]\frac{2y^2}{y}[/tex] - [tex]\frac{3xy}{y}[/tex] ( cancel y on numerator/ denominator of both fractions )

= 2y - 3x

I don’t know the answer so ignore the checked box

Answers

Answer:

CDHG

Step-by-step explanation:

Because you can go in that order and be able to get to the next letter. In the other option you cannot

hi can you help me in mate plis simplify the following algebraic expressions​

Answers

Answer:

[tex] \frac{3 {x}^{2} }{ {y}^{2} {z}^{6} } [/tex]

Step-by-step explanation:

I have attached the explanation above. hopefully this will help

3. Una forma de dividir facilmente entre 4 es dividiendo dos veces entre 2.Observa el ejemplo y aplica el procedimiento utilizado


Ejemplo: 568÷4=(568÷2)÷2
= 284 ÷2
= 142

a) 936÷4= c)2 812÷4=
b) 2 084÷4= d)3 720÷4=

Answers

Sbbshshshshhshsueieiee

please answer
HCF of 16 and 40

Answers

Answer:

8

Step-by-step explanation:

A soccer team made $575.75 from selling popcorn at a concession stand during a tournament. The popcom cost the
team $65.00. What is the amount of money earned for each player if the profit is divided equally among the 15
players? Round to the nearest cent.
O S34.05
0 $42.72
57.661.25
59.611.25 hurry I'm being timed!

Answers

Answer:

$34.05

Step-by-step explanation:

What is the slope of the line represented by the equation y-6 = 5(x-2)?
O A. 6
O B. 5
O C. -5
O D. 2

Answers

The slope is 5. For sure

Answer:

B

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 6 = 5(x - 2) ← is in point- slope form

with slope m = 5 → B

please tell me the answer to this, thanks

Answers

Step-by-step explanation:

Hey there!

The equation is: 2x + 3y -12=0 (i)

From the given equation;

Slope (m) = (-coeff.of X)/(coeff.of y)

m = -2/3

Now; Let the missing component be "a".

The equation also can be written in;

The equation also can be written in;(y-8) = -2/3(x-a) (using one point formula)

3y - 24 = -2x + 2a

2x +3y -2a -24 = 0………(ii)

Since both equation are made from same coordinates, equating equation (i) and (ii).

2x + 3y -12= 2x +3y -2a -24

Cancel like terms,

-2a - 24 = -12

or, -2a = 12

or, a = -6.

Therefore, the missing value is -6.

Check:

Putting the value "a" in equation (ii).

2x + 3y -2(-6) -24 = 0

or, 2x+3y -12 = 0 (which is equal to equation (i).

Hope it helps!

A college with a graduating class of 4000 students in the year 2010 predicts that its graduating class will grow 5% per year.
Using an exponential function to model the number of students y in the graduating class t years after 2010 to predict the number
of students in 2017?

Answers

Hello,

[tex]u_0=4000\\u_1=4000*1.05 (for\ year\ 2011)\\\\u_n=4000*1.05^n\\So:\\year\ 2017: u_7=4000*1.05^7=5628,401690625\ \approx{5628}[/tex]

Using an exponential function, the number of students y in the graduating class 7 years after 2010 i.e. in 2017 will be 5628.4

What is an exponential function?

y = abˣ, where a is the initial population, b is the rate, and x is the time, is the standard exponential function.

How to solve this problem?

Here initial student population = 4000.

Rate = 5% = (100 + 5)/100 = 1.05

Time = 7 years.

Now, in 2017, the population will be y = 4000 * (1.05)⁷ = 5628.401691 ≅ 5628.4.

Therefore, using an exponential function, the number of students y in the graduating class 7 years after 2010 i.e. in 2017 will be 5628.4

Learn more about exponential function here -

https://brainly.com/question/14551308

#SPJ2

Hello, Brainly community!

This question is for all of those Calculus people out there.

The volume of a swimming pool is changing with respect to time, such that the volume is given by W(t), where W(t) is measured in cubic centimeters and t is measured in seconds. A tangent line is shown for W(t) at t = 3 seconds. Determine the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
(I've narrowed down the answer choices to 2, and just really need to find the right way of thinking to find the answer)

(A) W(lim t) as t goes to 3.
(B) [W(3.1) - W(2.9)] / 0.2.

Thank you in advance!

Answers

Answer:

(B)  [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]

General Formulas and Concepts:

Calculus

Limits

Derivatives

The definition of a derivative is the slope of the tangent line.

Derivative Notation

Instantaneous Rates

Tangent Line: [tex]\displaystyle f'(x) = \frac{f(b) - f(a)}{b - a}[/tex]

Step-by-step explanation:

Since we are trying to find a rate at which W(t) changes, we must find the derivative at t = 3.

We are given 2 close answer choices that would have the same numerical answer but different meanings:

(A)  [tex]\displaystyle \lim_{t \to 3} W(t)[/tex](B)  [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]

If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the rate at which the volume would be changing and it is not a derivative.

If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a derivative at t = 3, and a derivative tells us what rate something is changing.

∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

Find the measure of the indicated angle.

Answers

2x + 40 = 180

2x = 140

x= 70

answer is 70

PLEASE HELP I'LL MARK BRANLIEST!
Activity Gina is playing dominoes with her family. She and her brother, Greg, are playing as a team (team A) against their parents (team B). The table shows how many points the two teams have scored in each round. Gina is keeping track of the scores and wants to know which measures of center and spread best represent each team’s data.

Team A: 15 20 15 5 10 15 10 15 5 20
Team B: 20 15 25 30 20 25 0 15 25 30

Part B What is the mean score for team A? Show your calculation.

Answers

Answer:

Mean of team A is 13

Step-by-step explanation:

I hope it helps:)

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