A particle moves along the x-axis so that time t>0 the position is given by x(t)=0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1. What is the velocity of the particle at the first instance the particle is at the origin?

Answers

Answer 1

The velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.

To find the velocity of the particle at the first instance it is at the origin, we need to find the value of t when x(t) = 0.

Since the particle is at the origin when x(t) = 0, we have:

[tex]0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1 = 0[/tex]

Using numerical methods or graphing the equation, we find that the roots are approximately t ≈ -0.618, t ≈ 1.532, t ≈ 3.143, and t ≈ 2.944.

Since t > 0, the first instance the particle is at the origin corresponds to t ≈ 2.944 (the smallest positive real root).

Now, to find the velocity of the particle at this instance, we need to find the derivative of the position function x(t) with respect to time t, which gives us the velocity function v(t):

v(t) = dx/dt

[tex]v(t) = d/dt (0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1)\\v(t) = 2t^3 - 4.5t^2 - 4t + 6[/tex]

Now, we can find the velocity at t ≈ 2.944:

[tex]v(t = 2.944) = 2(2.944)^3 - 4.5(2.944)^2 - 4(2.944) + 6[/tex]

v(t ≈ 2.944) ≈ 16.885

So, the velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.

learn more on velocity :

https://brainly.com/question/29290259

#SPJ4


Related Questions

Help pls I don’t understand this shi

Answers

Answer:

It's kind-of blurry, can you copy-paste the questions?

Step-by-step explanation:

Find each missing measure in the diagram below.
EF=(
m2F=d
3.
232
18 in
23
E
E

Answers

Answer:

EF= 18 in. , m<F=134'

Step-by-step explanation:

This ones for the boys with the booming system, top down ac with the cooling sytem

The dimensions of a right triangle are shown in the diagram.

What is the length of the missing side, to the nearest tenth of a centimeter?

Answers

Answer:

18.4 cm

Step-by-step explanation:

For this problem, you would use Pythagorean Theorem or a^2+b^2=c^2. Don't forget that the c in the formula is always your hypotenuse or the longest side of the triangle. The a and the b are always the legs of the triangle. (It doesn't matter which leg is which letter) The hypotenuse is also always across from the 90 degree angle. Picture the 90 degree angle as an arrow pointing to the hypotenuse.  In this case, the hypotenuse (or c) is 20.7 cm. Now all you have to do is plug and chug! I hope this helps you and thanks for asking your question!!

6. Five more than eight times a number is greater than four less than
seven times the number. Write an inequality to represent this relationship.
Then solve the inequality. *

Answers

8x+5 > 7x -4

X+5> -4

X> -9

Answer:

8x + 5 > 7x - 4

x > -9

Step-by-step explanation:

Five more than eight times a number

8x + 5

is greater than

>

four less than seven times the number

7x - 4

All together:

8x + 5 > 7x - 4

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

Solve:

Subtract 7x from both sides

x + 5 > -4

Subtract 5 from both sides

x > -9

recipe☝️
Question: How many cups of sifted cake flour will you need for 2 cakes? Show your work.​

Answers

Answer:

5 cups of flour need to make two cakes

what is 2/3 divided by 1/3

Answers

Answer:

2

Step-by-step explanation:

2/3 ÷ 1/3 =

2/3 • 3/1 =

6/3 =

2

The quotient is 2

which year in the 18th century was a perfect square

Answers

Answer:

THE dates dec. 6 1729, and june 4 1764 were the only two perfect square dates in the 18th century

What is the period of y=2cos(3x-2(3.14))?
A. 3(3.14)

B. 6(3.14)

C. 3(3.14)-2

D. 3(3.14)/3

Answers

Answer:

the correct answer is B

Step-by-step explanation:

I got it correct on 2021 edge

What is the range of the graphed function?
O [x1-2 O [yI-2 O {x | x is a real number}
O [vl y is a real number}

Answers

Answer:

first one my sister tried it

Step-by-step explanation:

Pete saw that he was 200 yards from shore when he dove out of the boat. It took him 49 seconds to swim the first 50 yards. At that rate, how much longer will it take to reach the shore?
tysm<3

Answers

Answer:

147 seconds to get to the shore(after the 49 seconds)

Step-by-step explanation:

If Pete swam at a constant speed of 50 yards/49 seconds, you just have to multiply that by four, to get 200 yards. If you want the total time from his boat to shore, that is 196. If you want how much longer it would be, it would be 147 seconds

for minutes, just divide by 60

I want you to set a goal of signing up 25% of your new customers for our new service feature." Representative: "If I get 96 new customers that means I have to get

Answers

If he get 96 new customers that means he will have to sign 24 customers

for the new service features.

The deal is to get 25% of your new customer to sign the new service features.

When the new customers are 96 in numbers, the number of individuals(25%

of the new customers) to be signed for the new features can be calculated as

follows:

New customer to sign for the new features = 25% of 96

New customer to sign for the new features = 25 / 100 × 96

New customer to sign for the new features = 2400 / 100

New customer to sign for the new features = 24

read more: https://brainly.com/question/19540991?referrer=searchResults

This means that if I get 96 new customers that means I have to get 24 new customers

From the question, I want to set a goal of signing up 25% of your new customers for our new service feature.

Since we have 96 new customers, hence the total amount of new customers needed will be expressed as:

= 25% of 96

= 0.25 * 96

= 24 new customers

This means that if I get 96 new customers that means I have to get 24 new customers

Learn more on proportion here: https://brainly.com/question/19914553

Liam invests $3,670 in a savings account at his local bank which gives 1.9% simple annual interest. He also invests $2,040 in an online savings account which gives 5.5% simple annual interest. After five years, which one will have earned more interest, and how much more interest will it have earned, to the nearest dollar?

Answers

Step-by-step explanation:

Given:

Investment P₁ = $3670Investment P₂ = $2040Rate of interest r₁ = 1.9% SIRate of interest r₂ = 5.5% SITime t = 5 years

Find amount of interest in both investments:

I₁ = P₁r₁t = $3670*(1.9/100)*5 = $348.65I₂ = P₂r₂t = $2040*(5.5/100)*5 = $561.00

As we see the online savings account earns more interest and the difference is:

$561.00 - $348.65 = $212.35 ≈ $212

48 mouse traps/6 people = X mouse traps/1 person

Answers

Answer:

8 mousetraps

Step-by-step explanation:

to find how many mousetraps per person, we need to divide 48 by 6, which gives us 8.

Identify the similar triangles.
ΔHFE=
ΔHFE=​

Answers

∆HFE is similar to ∆HFG and ∆ HEG (they all are right triangles and have the same, shape.)

The given triangle ΔHFE is similar to triangle GFH and triangle GHE.

What are similar triangles?

Similar triangles are two triangles that have the same shape but may differ in size. They have corresponding angles that are congruent and corresponding sides that are proportional.

Here,

Since triangle HFE is similar to triangle GFH,
∠HEF = ∠GHF,
∠FHE = ∠HGF, and ∠HFE = ∠HFG

Similarly

ΔHFE is similar to triangle ΔGHE.

Similar triangles are useful in many areas of mathematics and in the real world, such as in architecture, engineering, and cartography, where they are used to make scale models of buildings and other structures.

Thus, the given triangle ΔHFE is similar to triangle GFH and triangle GHE.

Learn more about similar triangles here:

https://brainly.com/question/12101336
#SPJ2

can someone help
me on one of these please!

Answers

For number 13, there is no change. It is 0. The equation is x=7 since the line is on x and not y. The y intercept is 0.

Please help make sure to show your steps too, please

Answers

Answer:

Slope = -2

Step-by-step explanation:

Given the two points, (-4, 10) and (0, 2), the error in the given problem is the incorrect substitution of values into the formula. It should have been formatted as follows:

Let (x₁, y₁) = (-4, 10)

    (x₂, y₂) = (0, 2)

The formula for solving for the slope of the line is:

m = (y₂ - y₁)/(x₂ - x₁)

where m represents the slope of the line.

Substitute the given values into the formula to solve for the slope:

m = (y₂ - y₁)/(x₂ - x₁)

[tex]m = \frac{2 - 10}{0 - (-4)}[/tex]

[tex]m = \frac{-8}{0 + 4 }[/tex]

m = -8/4

m = -2

Therefore, the slope of the line is -2.

Wendy was riding her bike along a trail and travelled 63 miles in 6 hours. When Iman was riding on the same trail she travelled 10.1 miles per hour. What was Wendy's unit rate for her bike ride? (Miles per Hour) Who was riding faster?

Answers

Wendy was going faster at 10.5 mph.

To find mph, you divide the distance by the time. 63 divided by 6 is 10.5, which is faster than 10.1

Jessica bought a soft drink for 4 dollars and 5 candy bars. She spent a total of 19 dollars. How much did each candy bar cost ?

Answers

Answer:

$3

Step-by-step explanation:

19-4= 15

15 divided by 5= 3

PRETTY PLS HELP ME JUST 2 MORE QUESTIONS PLS 50 POINTS

Answers

Answer:

I think that you should take your time and answer, every one can help you

Step-by-step explanation:

Step-by-step explanation:

ok give question and intro new sis

What percent of the bottle of apple juice is water?

Answers

percent of water is: 32/80*100= 40%

Rewrite the equation below so that it does not have fractions.

3/4x-5=3/8

Do not use decimals in your answer.

Answers

Answer:

x=  

6

43

 

Step-by-step explanation:

pasos  

4

3

x−5=  

8

3

Agrega 5 a ambos lados.

4

3

x=  

8

3

+5

Convertir 5 a la fracción  

8

40

.

4

3

x=  

8

3

+  

8

40

 

Como  

8

3

 y  

8

40

 tienen el mismo denominador, sume sus numeradores para sumarlos.

4

3

x=  

8

3+40

 

Suma 3 y 40 para obtener 43.

4

3

x=  

8

43

 

Multiplica los dos lados por  

3

4

, el recíproco de  

4

3

.

x=  

8

43

×(  

3

4

)

Multiplica  

8

43

 por  

3

4

 (para hacerlo, multiplica el numerador por el numerador y el denominador por el denominador).

x=  

8×3

43×4

 

Realiza las multiplicaciones en la fracción  

8×3

43×4

.

x=  

24

172

 

Reduzca la fracción  

24

172

 a su mínima expresión extrayendo y anulando 4.

x=  

6

43

 

6x=43 should be the answer

Divide 2200kg in the ratio 5: 6.​

Answers

Answer:

i have no idea1233930494

What is the best estimate for the volume of a jug of milk?

Answers

Answer:

3.785 litres

Step-by-step explanation:

Wjejjejjsnsbbnxkskakksnsnsnznsmsnndndd

Answers

Answer:

whats

Step-by-step explanation:

[tex]\orange{\rule{40pt}{555555pt}} \green{\rule{40pt}{555555pt}} \blue{\rule{40pt}{555555pt}} \red{\rule{40pt}{555555pt}}\pink{\rule{40pt}{555555pt}}\yellow{\rule{40pt}{555555pt}}[/tex]

The perimeter of a rectangle is 78 units. The length is 5 units more than the width. Find the length.

Answers

Answer:

W = 8.5 units; L = 30.5 units

Step-by-step explanation:

The formula for the perimeter of a rectangle is P = 2L and 2W, where L and W represent the length and the width respectively.  Here, L = 3W + 5.  Adapting the formula P = 2L and 2W, we get: 78 = 2L + 2W  =  2(3W + 5) + 2W, or 6W + 10 + 2W = 78, or 8W = 68, or W = 68/8 = 8.5 units If W = 8.5 units, then L = 3(8.5 units) + 5 units = 30.5 units  

how did you get m in the equation

Answers

to get m in an equation u find it in y=mx+b

8th Grade Math
Janelle is saving $6 per week to buy a new bike. she has $85 on week five. How do you write this in slope intercept form?

Answers

Let y-axis saving
X-axis weeks
Slope change in y-axis/x-axis
If at week 5 she has 85
85=6(5)+C
C=55
Y=6x+55

The lengths of the sides of a triangle are square root 139, square root 73, and 6. Classify the trianglo as “acute", "right", or "obtuso".
Choose the correct type of triangle below.
O acute
obtuse
Oright

Answers

Answer:

It's obtuse.

Step-by-step explanation:

Mumble. Smells al-kashi laws of cosine to me.

[tex]a^2-b^2-c^2 = -2bc cos\alpha\\b^2-c^2-a^2=-2ca cos \beta\\c^2-a^2-b^2=-ab cos \gamma[/tex]

Now, we don't need to calculate the RHSs, and then:

If at least one of the three LHSs is greater than zero, the triangle is obtuse

If at least one is zero, it's a right triangle (pythagorean theorem anyone?)

if all three numbers are less than zero, the triangle is acute

Start crunching numbers.

[tex]139-73-36 = 30[/tex] First try was  the charm. finding 30 means that the product [tex][-2(\sqrt{73})(6) ]cos \alpha[/tex] is positive, and since the product in the large bracket is negative, the cosine has to be 0, thus the angle has to be greater than 90°, QED

Rachel has a $23,000 six year loan with APR of 7.25%

Answers

Answer:6,000 is the answer

Step-by-step explanation:

1.
What is the sum of
4 |
22 (1 point)
+
+
3
011
o

IN IN NII am |
0
0 0

Answers

Answer:

B. One whole number one over two. 1½

Other Questions
Each team tries to score more points.....win the Each team tries to score more points...to win the match. (in spite of/in order to/so that) c.The family purchased refreshments and spent a total of $18.50. If the total amount of money spenton tickets and refreshments was $94.50, use an equation to find the cost of one regular admissionticket.How would you write the equation? Complete the equation to calculate the cost of the portable speaker, including sales tax.$53= % of $50 Which is equivalent to 43will mark brainlist if right 2- The Dragon in Asian culture can be a symbol of:A- love and tranquilityB- Wisdom and enlightenment 170 students or 85% of the students went to attend college what are the total number of students? what is the simplest from of the ratio 40:16 ? Why did a revolution occur in Russia -18 = 3 (-z + 6) + 2z -0.75___-3/4which one is greater What is the coefficient of the first term in this expression?4r+q3r2+8q2r breathing involves the movement of diaphragm and Rib cagetrue or false What different cultures celebrate thanksgiving differently? Who names the Max/Kevin duo as "Freak the Mighty"Question 8 options:MaxThe policeKevinGram Name examples of primary sources and secondary sources. What is considered a pure substance? if you help me you get brainly need help w this question Escribe a tu amigo(a) tres preguntas sobre lo que el/ella y su familia hicieron durantelas vacaciones. Usa las expresiones de la lista y palabras interrogrativas, como: cundo,dnde, adnde, qu, quin, cul(es), y cuntos. (Write about your vacation.)comprartomar fotosmandarhablarmontarviajarvisitaracamparCundo acampaste? (need this answered in a sentence) Solve the math problem Only solve 3 and 4