A particle moves along the x-axis so that at time t ≥ 0 its position is given by x(t) = 2t3 - 21t2 + 72t - 53. At what time t is the particle at rest?

Answers

Answer 1

Step-by-step explanation:

The particle is at rest when the derivative of x(t), which is its velocity, is zero, i.e.,

[tex]\dfrac{d}{dt}[x(t)] = \dot{x}(t) = 0[/tex]

Since [tex]x(t) = 2t^3 - 21t^2 + 72t - 53,[/tex] its derivative is

[tex]\dot{x}(t) = 6t^2 - 42t + 72[/tex]

Equating this to zero, we get

[tex]6t^2 - 42t + 72 = 0 \Rightarrow t^2 - 7t + 12 = 0[/tex]

This is a familiar quadratic equation whose roots are

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

[tex]\;\;\;= \dfrac{7 \pm \sqrt{(7)^2 - 4(1)(12)}}{2}[/tex]

[tex]\;\;\;= \dfrac{7 \pm 1}{2}[/tex]

[tex]\;\;\;= 3\;\text{and}\;4[/tex]

This means that the particle will be at rest at t = 3 and t= 4.


Related Questions

3. Tom's entered a snowman building contest in which the person who builds the tallest
snowman wins. Currently, the record is 13.4 feet high. If Tom's snowman is currently 9 feet
high, how many more feet does he need to build on, in order to win the competition

Answers

tom's snowman has to increase by anything greater than 4.4 ft

Answer:

4.5 feet

Step-by-step explanation:

9+4.5=13.5

13.5>13.4


Find the future value of $124,357 deposited at 8% compounded quarterly for 4 years

Answers

Answer:

Future value, $63,398.79; Interest, $16,798.79

Step-by-step explanation:

Can anyone please help me answer this Math question ? As soon as possible !


The We-Make-It factory in the United States pays its 250 workers an average of $21 per hour, including benefits. The average number of work hours per employee in a year is 1,924. The owners of the factory are considering relocating overseas to a country where they can pay workers an average of $6 per hour, including benefits, to achieve the same production levels. Assuming that the company would hire the same number of workers for the same number of hours in a new location, how much could We-Make-It save in wages alone in the first year by moving to the proposed overseas location?

Answers

Assuming that this would not be destroying the lives of many in a community by locating overseas. The factory would save $2,886,000 in payroll wages during the first year of relocation.

Step-by-step explanation:

$15 saved in wages/working hour × 250 workers × 1924 hours per year/worker = $2,886,000

Simplify the following expression.

Answers

Answer:

-1

Step-by-step explanation:

[tex]3 + \sqrt{10 - {3}^{2} } + - 5 \\ = 3 + \sqrt{10 - 9} - 5 \\ = 3 + \sqrt{1} - 5 \\ = 3 + 1 - 5 \\ = 4 - 5 \\ = - 1[/tex]

Answer:

-1

Hope you could get an idea from here.

Doubt clarification - use comment section.

PLEASE HELP IMMEDIATELY
THANN YOU!

(Image attached above)

Answers

Answer: x = 2, explanation below

area of rectangles and squares is l * h or h * l (h is height and l is length)

length of left rectangle/square is

4*(6x+6) and for the right quadrilateral, it is 4x*9

4x*9 is 36x

and we use the distributive property for 4*(6x+6)

4*6x+4*6

4*6x = 24x

4*6 = 24

24x+24

They have equal areas, so we can make an equation making their areas equal.

36x = 24x+24

Subtract 24x from both sides

12x=24

divide 12 by both sides

x = 2

Step-by-step explanation:

A bus traveling at a constant rate of 50 miles per hour. At this rate, how far will the bus travel 3 1/4 hours?

Answers

First, let's do the easy part! Multiplying 50 by 3 will give us how far the bus would travel in 3 hours. 50 x 3 = 150.

Now let's do the quarter. 50 / 4 = 12.5. Simply add these two together now!

The bus will travel 162.5 miles!

Hope this helps :)

Find the volume
of the rectangular prism.
3 m
7 m
4 m

Answers

Answer:

The volume is 63m³

Step-by-step explanation:

Multiply all sides together so 4 x 7 is 21, 21 x 3 is 63.

l•w•h= 4•7•3 = 84. good luck

Help I’m so confused

Answers

Answer:

5x: linear; monomial

-7: constant; monomial

x^2 + 4: quadratic, binomial

x^2 - 3x + 11: quadratic, trinomial

2x - 9: linear, binomial

Step-by-step explanation:

Name using degree: just count the highest number of variables in a single term. if it's 0, its a constant polynomial, if it's 1 it's linear, 2 quadratic, 3 cubic

Name using number of terms: just count the number of "things" added or subtracted. If there's one, it's a monomial, two: binomial, three: trinomial.

23+4⋅2−7

the 23 is 2 to the third power.

Answers

Answer:

12618

Step-by-step explanation:

23x23x23=12617

4•2=8

12617+8=12625

12625-7=12618

Answer: 9

Step-by-step explanation:

The correct answer to [tex]2^{3} + 4[/tex] ⋅ [tex]2 - 7 = 9[/tex]

I hope that helps :)

The Greens are moving. Their real estate agent located 79 houses listed for sale in their price range. Of those bouses listed for sale: 49 had a finished basement. 56 had a three car garage. 37 had a finished basement. How many had a finished bsement but not a three car garage?

Answers

I think 5 steps is right I hope it help if it is not right I am sorry

Francine recorded today's high
temperature as 78.6°F. Today's low
temperature was 4.7°F less than
that. How much cooler was today's
low temperature than yesterdays low
temperature, which was 77.4°F?

Answers

Answer:

3.5

Step-by-step explanation:

the problem says 4.7 less than which refers to subtraction so we can plug our numbers into a subtraction problem like so

78.6-4.7 which equals 73.9

the second part of the problem asks the difference between yesterday's low and today's.

we can take the two lows and subtraction them to find this answer.

77.4-73.9 which equals 3.5

so today's low was 3.5 degrees cooler than yesturdays

f (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20

Three roots of this polynomial function are −1, 1, and 3 + i.

Which of the following describes the number and nature of all the roots of this function?


f (x) has two real roots and one imaginary root.

f (x) has three real roots.

f (x) has five real roots.

f (x) has three real roots and two imaginary roots.

Answers

Answer:

  f(x) has three real roots and two imaginary roots.

Step-by-step explanation:

The function is degree 5, so will have 5 roots in total. 2 real roots and one complex root are shown. Complex roots come in pairs, so there will be one more, but cannot be two more.

  f(x) has three real roots and two imaginary roots.

__

All five roots must be accounted for. This leaves out the first two choices. The given complex root eliminates the third choice.

Answer:

D

Step-by-step explanation:

did the test

Consider points a, b, and c in the graph below. Determine which of these points are relative maxima on the interval x = 1 to x = 3

Answers

Answer:

c

Step-by-step explanation:

Relative Maxima means "a point that is higher than the points directly beside it on both sides", or when looking at derivatives, when the derivative of a function changes from above zero to below zero. If you're looking at a graph, all you have to do is find those points that seem to be poking out of the graph, aka c, when x=2.

Also look at the interval - (1,3), so... really, just by that, c would be your answer

PLEASE HELP ME PLEASE

Answers

Answer:

5

Step-by-step explanation:

50 POINTS!!!
Which is the graph of linear inequality x - 2y = -12?

Answers

Bottom one
I think or not the first one

12+13×4 what is the answer best explanation will get brainliest​

Answers

64

Multiply 13 by 4

12 + 52

Add 12 and 52

64

Hello there, this is just a basic PEMDAS problem

[tex]{\huge{\boxed{\mathbb{QUESTION}}}[/tex]

12+13×4 what is the answer

[tex]{\huge{\boxed{\mathbb{EQUATION}}}[/tex]

[tex]12+13\cdot4[/tex]

_______________

[tex]{\huge{\boxed{\mathbb{PEMDAS\:RULE}}[/tex]

Follow PEMDAS rule

Parenthesis Exponents Multiplication or Division Addition or Subtraction

_______________

So first we will multiply [tex]13[/tex] by [tex]4[/tex] giving us [tex]52[/tex]. Now just add [tex]12+52=64[/tex]

_______________

[tex]{\huge{\boxed{\mathbb{ANSWER}}[/tex]

64

Consider the following data for 120 mathematics students at a college concerning the languages French, German, and Russian:
65 study French, 45 study German,
42 study Russian , 20 study French and German,
25 study French and Russian,
15 study German and Russian.
8 study all three languages.
Determine how many students study exactly 1 subject and fill the correct numbers of students in each eight region of Venn diagram shown in figure.

Answers

Answer:

check online for more information

The Venn diagram for given situation is as shown below.

The number of students who study exactly one subject = 56

What is set?

"It is a collection of well-defined elements"

What is Venn diagram?

"It is a pictorial representation that uses circles to show the relationships among sets."

For given example,

We have been given the data for 120 mathematics students at a college concerning the languages French, German, and Russian

Let set A, B and C represents the number of students who study French, German and Russian respectively.

⇒ n(A) = 65

⇒ n(B) = 45

⇒ n(C) = 42

20 study French and German

⇒ n(A ∩ B) = 20

25 study French and Russian,

⇒ n (A ∩ C) = 25

15 study German and Russian.

⇒ n(B ∩ C) = 15

8 study all three languages.

⇒ n(A ∩ B ∩ C) = 8

So, the Venn diagram for given situation is shown below.

Now, we find the number of students who study exactly one subject.

28 students study French only, 18 students study German only and 10 students study Russian only.

So, the total number of students who study exactly one subject is,

28 + 18 + 10 = 56

Therefore, 56 students study exactly one subject

Learn more about Venn diagram here:

https://brainly.com/question/1605100

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after a party 3/4 cake is leftover. Dennis eats 1/2 of the leftover cake. Which fraction model represents the amount of cake Dennis eats?​

Answers

8/8-5/8 = 3/8 Which Is Equivalent To The Amount Of Cake Left Over And The Amount Of Cake That Dennis Ate

Which of the number line graphs shows the solution set of |x – 2| > 3?

Answers

Answer:

I have it!

Step-by-step explanation:

The question is in the picture​

Answers

Answer:

8

Step-by-step explanation:

The answer is 8 units

Determine the area of the yellow sector

Answers

Answer:

146 is the answer im positive

Today is my birthday. My age today, in months, is 72 times my age 5 years ago,
in years. My age today, in years, is

Answers

Answer:

Happy Birthday!

Step-by-step explanation:

evaluate the following expression . 2*[4+(12+16)/7

Answers

Answer:

16

Step-by-step explanation:

[tex]2 \times (4 + (12 + 16) \div 7 \\ (12 + 16) = 28 \div 7 = 4 + 4 = 8 \\ 2 \times 8 = 16[/tex]

Question : Explore criteria of congruency of triangles using a set of triangle cut outs

Answers

Answer:

       Explore Various Criteria for Congruence TrianglesSASASAAASSSSRHS

If the ratio y/x is the same for all related pairs of x and y, what does that mean about the relationship between x and y?

Answers

Answer:

The the relationship is linear

Step-by-step explanation:

If y/x is same for all pairs of x and y, slope is a constant value that is not changed by value of x or y. Hence, it is linear function.

HURRY HELP PLEASE! SERIOUS ANSWERS ONLY!


Living Space?

You have the opportunity to live in a 3 bedroom 3.5 bath on Miami Beach in a Luxury Condo or in Laurel Mississippi in a 5-bedroom 7 bath home. Money for either is not an issue. The only stipulation is that you and your present family situation will remain intact. Given your present situation, which would you choose and why? (Students will receive full credit for their completion of the project; steps 2 and 3)

1. Look up property and amenities

a. Condo on: unaresidencemiami.com/price-list

b. Home on: 2230 Ridgewood Dr, Laurel, MS 39440 (type in address)

2. Look up the community in which EACH is located

3. Solve for the intersection of the two properties (two variable systems of equations using the

cost and the Square Footage as the variables)

a. Condo: $2.2 million / 1946 sq feet

b. House : $.3 million / 4681 sq feet

4. Which would you choose and why?

Answers

Answer:

The Mississippi home

Step-by-step explanation:

I would get the Mississippi home because it has 5 bedrooms with 7 bathrooms, it would be a great home for a family and guest to go to. and it also depends on the condition of the home and the amount of people in you family.

Air is being pumped into a spherical balloon at the rate of 7 cm3/sec. What
is the rate of change of the radius at the in stant the volume equals 36π cm3
? The volume of
the sphere of radius r is (4 over PI )r power of 3

Answers

Answer:

Step-by-step explanation:

[tex]V=\frac{4}{3} \pi r^3\\\frac{dV}{dt} =\frac{4}{3} ~\pi \times ~3r^2\frac{dr}{dt} \\\frac{dV}{dt} =4\pi r^2\frac{dr}{dt} \\7=4\pi r^2\frac{dr}{dt} \\\frac{dr}{dt} =\frac{7}{4\pi r^2} \\when~V=36 \pi cm^3\\36\pi =\frac{4}{3} \pi r^3\\r^3=\frac{36\pi \times 3}{4\pi } =27=3^3\\r=3~cm\\\frac{dr}{dt} =\frac{7}{4\pi \tmes 3^2} \\\frac{dr}{dt} =\frac{7}{36 \pi } cm/sec[/tex]

(X+2b)(x-4b) simplified

Answers

Answer:

I will ASSUME X = x

x² + 2bx - 4bx - 8b²

x² - 2bx - 8b²

Answer:

[tex]\\\\\\-8b^2-2bx+x^2[/tex]

Step-by-step explanation:

[tex](x+2b)(x-4b)\\=(x+2b)(x+(-4b)\\=(x)(x)+(x)(-4b)+(2b)(x)+(2b)(-4b)\\\\x^2-4bx+2bx-8b^2\\\\-8b^2-2bx+x^2[/tex]

Don has seven pairs of​ shoes, three pairs of​ pants, and six shirts. If all items are​ compatible, how many different outfits can he​ wear?

Answers

Answer:

126

Step-by-step explanation:

There are 126 different ways he can wear the outfit.

What is Combination?

The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words indicates "Selection of things," where the order of the items is irrelevant.

Given:

Number of pairs of shoes= 7

Pants= 3 pairs

Shirts= 6

So, different outfits can he​ wear

= 7 x 3 x 6

= 21 x 6

= 126

Hence, there 126 different ways he can wear the outfit.

Learn more about combination here:

https://brainly.com/question/8969582

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PLSS Someone plss help plss helppp plllsss Will mark brainliest!!!

Answers

Answer:

( 6 , 8 )

Step-by-step explanation:

y = kx

k = [tex]\frac{y}{x}[/tex]

( 3 , 4 )

k = [tex]\frac{4}{3}[/tex]

[tex]\frac{4}{3}[/tex] = [tex]\frac{8}{6}[/tex] = [tex]\frac{12}{9}[/tex] = ....

( 6 , 8 )

Other Questions
Find the value of x and the indicated angles. Complete the table using the equation y = 5x + 3. x -1 0 1 2 3 y -? ? ? ? ? Please help meee :( Just an answer Presented below are selected transactions for Werley Company for 2021. Jan. 1 Received $9,000 scrap value on retirement of machinery that was purchased on January 1, 2011. The machine cost $90,000 on that date, and had a useful life of 10 years with no salvage value. April 30 Sold equipment for $34,000 that was purchased on January 1, 2018. The equipment cost $90,000, and had a useful life of 5 years with no salvage value. Dec. 31 Discarded a business truck that was purchased on April 1, 2017. The truck cost $27,000 and was depreciated on a 5-year useful life with a salvage value of $2,000. Journalize all entries required as a result of the above transactions. Werley Company uses the straight-line method of depreciation and has recorded depreciation through December 31, 2020. (Credit account titles are automatically indented when the amount is entered. Do not indent manually. Record journal entries in the order presented in the problem. If no entry is required, select "No Entry" for the account titles and enter 0 for the amounts.) Date Account Titles and Explanation Debit Credit choose a transaction date Jan. 1 enter an account title to record depreciation expense enter a debit amount enter a credit amount enter an account title to record depreciation expense enter a debit amount enter a credit amount enter an account title to record depreciation expense enter a debit amount enter a credit amount enter an account title to record depreciation expense enter a debit amount enter a credit amount choose a transaction date April 30 enter an account title to record depreciation expense enter a debit amount enter a credit amount enter an account title to record depreciation expense enter a debit amount enter a credit amount (To record depreciation expense) choose a transaction date April 30 enter an account title to record sale of equipment Cash enter a debit amount 34000 enter a credit amount enter an account title to record sale of equipment Accumulated Depreciation-Equipment enter a debit amount Miranda bought oranges which are sold in a bag of 5 for $2. The next day she bought 20 oranges which was $8. What is the table for this problem? (Create a table with the information above with at least 5 ordered pairs) Have you visited any museum?If yes,describe it in five sentences. Anyone?? What is the correct factorization of x^2 - 2x - 15?HURRRYYYY PLS A. 4 B. 5C.8 D.12 I need help asap!!Triangle 1 is composed of line segments AB, BC, and CA.Triangle 2 is composed of line segments DE, EF, and FD.The triangles are similar with a scale of 5:2.Select the true statement about the proportions of the sides. 2.In a box of 80 glasses, 3 are broken.Work out the percentage of broken glasses in the box. the name of the building above? 3 examples of how you think cells work in living things. ASAPPPPP!!!Why do cells have a high surface area to volume ratio? *A. to contain more nutrientsB. to contain more organellesC. to more readily exchange substances across the cell.D. to have only small substances travel across the cell. What equipment is generally used to make lyophilized medications suitable for administering to the patient? a) Test tubes or sterile ampules O b) Petri dishes and sterile droppers c) Sterile syringes or graduated cylinders d) Measuring cups and clean, warm water Explain the importance of scientific names. HELP LOTS OF POINTS!! Which information in the accounts payable subsidiary journal is entered afterthe amount of credit or debit?A. The name of the vendor B. The terms of the sale C. The balanceD. The date Arial Company has two products: A and B. The company uses activity-based costing. The total cost and activity for each of the company's three activity cost pools are as follows: Total ActivityActivity Cost Pool Total Cost Product A Product B TotalActivity 1 $22,000 400 100 500Activity 2 $16,240 380 200 580Activity 3 $14,600 500 250 750The activity rate under the activity-based costing system for Activity 3 is closest to:a. $70.45b. $28.87c. $19.47d. $58.40e. $32.5 Help help math pelsss please please How to factor 10n^2 +n -3and 2d^2=8de+6e^2 How to write a chemical formula ? What is a complex sentence for the word infinitesimal?