A particle moves along the x-axis so that at time t≥0t\ge 0t≥0 its position is given by x(t)=−t3+6t2−9t+42.x(t)=-t^3+6t^2-9t+42.x(t)=−t3+6t2−9t+42. Determine the total distance traveled by the particle from 0≤t≤4.0\le t \le 4.0≤t≤4.

Answers

Answer 1

Answer: 4 units

Step-by-step explanation:

The given position function: [tex]x(t)=-t^3+6t^2-9t+42.[/tex], where t≥0.

To determine:  Total distance traveled by the particle from 0≤ t ≤ 4.0.

At t=0,

[tex]x(0)=-(0)^3+6(0)^2-9(0)+42=42\\[/tex]

At, t=4,

[tex]x(4)=-(4)^3+6(4)^2-9(4)+42\\\\=-64+6(16)-36+42=38[/tex]

Total distance traveled by the particle from 0≤ t ≤ 4.0 = |42-38| units

= 4 units

Hence, the distance traveled by the particle from 0≤t≤4.0 is 4 units.


Related Questions

simplify the fraction completly
75/100

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The simplest form for 75/100 is 3/4
It’s 3/4. Mark me brainiest if I’m right plz

need help someone !!!!!!!!

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it contains from 2 pieces:
1) y=x+1, -2=
2) y=2, 1<=x<=4

help!! i added the attachment

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P= 1
You do 15p+58=9p+64

What is the quotient?

-4/5➗2

Answers

The answer is -0.4 because I just did it in a calculator.

What are the dimensions of a 2x4x8

Answers

Answer:   Many of you know this, but why is this a thing? You don't go to Subway and pay for a $5-footlong expecting to get 11 inches (although many of you will argue this is the case). And it's not just a 2x4: A 1x4 is actually ¾ inches by 3-½ inches; a 4x4 is actually 3-½ inches by 3-½ inches.

Step-by-step explanation:

If you are asking what they equal up too, your answer is 16

If this isn't, please correct me and I will give you a better answer

Martha deposited $385.25 into her bank account. After her deposit, there was $832.48 in Martha's account. How much money did Martha have in her account before the deposit?

Answers

Answer:

447.23

Step-by-step explanation:

832.48 - 385.25

I need help on this please

Answers

Answer:

x = 60°

y = 60°

Step-by-step explanation:

It's an equilateral triangle, all angles are congruent.

Solve the following inequality: -3x - 8 > -32

Answers

Answer:

x < 8

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

A rectangular window has a width of 3.5 yards and a length of 4.5 yards what is the perimeter of the window in yards

Answers

Answer:

16 yards

Step-by-step explanation:

Perimeter = 3.5 + 3.5 + 4.5 + 4.5

Perimeter = 16 yards

Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2 l plus 2 w equals 62 to find the width of the run.

Which statements are true of the solution? Check all that apply.

The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.

Answers

Answer:

The answers you guys are looking for are C, D, and E

Step-by-step explanation:

I dont have one. :)

The true statements include

(c) The value of w cannot be a negative number.(d) Substitution is used to replace the variable l with a value of 20.(e) The subtraction property of equality is used to isolate the term with the variable w.

How to determine the true statements?

The equation is given as:

2l + 2w = 62

Where:

l = 20

Substitute l = 20

2 * 20 + 2w = 62

Evaluate

40 + 2w = 62

Subtract 40 from both sides

2w = 22

Divide both sides by 2

w = 11

The above computation means that the true statements include (c), (d) and (e)

Read more about perimeter at:

https://brainly.com/question/24571594

#SPJ2

need help fast im giving 20 points

Answers

Answer:

c

Step-by-step explanation:

What is the right answer for the ordered pairs?

Answers

Answer:

D. (2, -3) and E. (4,-1)

Step-by-step explanation:

In quadrant IV, the possible x-coordinate that can be gotten can only be positive, while the possible y-coordinate can only be a negative value. Thus, the coordinate pair we can get is a positive x-coory and a negative y-coordinate (x, -y).

Therefore, from the list of options given, the two ordered pairs that belong in Quadrant IV are D. (2, -3) and E. (4,-1)

Can a parallelogram also be a rectangle

Answers

Answer:

yes

Step-by-step explanation:

Answer:

sometimes

Step-by-step explanation:

What is the better buy? 2 for $3.00 (Or) 8 For $12.40

Answers

Answer:I say 8 for $12.40

Step-by-step explanation:

Answer:

8 for 12.50

Step-by-step explanation:

12.50/8 = 1.55

3.00/2= 1.50

youre getting 6 more pens for only 5 cents more

which of the following can be a Pythagorean triplets?:

a) 2cm 2cm ,4cm b) 5cm, 12cm ,13cm c) 3cm ,5cm ,6cm d) 7cm, 4cm 5 cm.


need full solution
or I'll report ​

Answers

Answer :-

As we know that,

Pythagoras triplet

1) a² + b² = c²

Let

[tex]\sf \: {2}^{2} + {2}^{2} = {4}^{2}[/tex]

[tex]\sf \: 4 + 4 = 16[/tex]

8 ≠ 16Hence, A can't be Pythagoras triplet

2) a² + b² = c²

[tex]\sf \:5 {}^{2} + {12}^{2} = {13}^{2}[/tex]

[tex]\sf \: 25 + 144 = 169[/tex]

169 = 169Therefore, B can be Pythagoras triplet

3)a² + b² = c²

[tex]\sf {3}^{2} + {5}^{2} = {6}^{2}[/tex]

[tex]\sf 9 + 25 = 36[/tex]

34 ≠ 36Hence, C can't be Pythagoras triplet

4) a² + b² = c²

[tex]\sf {5}^{2} + {4}^{2} = {7}^{2}[/tex]

[tex]\sf \: 25 + 16 = 49[/tex]

41 ≠ 49Hence, D can't be Pythagoras triplet

Therefore :-

Only B can be Pythagoras triplet.

Write the equation of a line that passes through the point (4, -2) and is perpendicular to y = 3.

Answers

Answer:

x = 4

Step-by-step explanation:

When something is perpendicular, it must form a 90° or right angle [it will make a square]. Also keep in mind that perpendicular lines have reciprocal [numerator and denominator switch] slopes [steepness]

If you are given a line with a slope of zero like y = 3, any given line of x will be perpendicular. This is because when y = n; x is undefined. When x = n ; y is undefined. Since you want a line that will go through point (4, -2) and will be perpendicular to y = 3, just set x to the value of x in the coordinate. And in this case x is 4 so x = 4 will be the equation.

Please do both questions and explain
I'll give brainliest

Answers

9514 1404 393

Answer:

  12√2

  24√2

Step-by-step explanation:

The Pythagorean theorem tells you the square of the slant length is the sum of the squares of x and the height:

  (6√11)^2 = x^2 + (6√3)^2

  x^2 = 36·11 -36·3 = 36·8 = 144·2

  x = 12√2 . . . . length of 1/2 the house

The full length of the house is double this value:

  2x = 24√2 . . . . full length of the house

inverse equation x-19 = -23

Answers

Answer:

Isolate the X by adding 19 on both sides sicne the invers of -19 is 19

-23+19= -4

now you’d get

x= -4 since its a one step equation and X is isolated

WRITE THE FIRST 4 TERMS OF THE SEQUENCE DEFINED BY THE GIVEN RULE ( PLEASE ANSWER FAST PLEASE QUICKLY WILL GIVE BRAINLIEST AND THANKS!!!! PLEASE HURRY!!!!)

Answers

Step-by-step explanation:

5.) f(1) = 7, f(n) = -4※f(n-1) + 15

[tex]f(2) = - 4 \times 7 + 15 = - 13 \\ f(3) = - 4 \times ( - 13) + 15 = 67 \\ f(4) = - 4 \times 67 + 15 = - 253[/tex]

The first four terms are 7, -13, 67, -253.

7.) f(1) = 3, f(n) = [f(n-1)]²

[tex]f(2) = (3)^{2} = 9 \\ f(3) = ( {9)}^{2} = 81 \\ f(4) = ( {81)}^{2} = 6561[/tex]

The first four terms are 3, 9, 81, 6561.

The failure of a circuit board interrupts work that utilizes a computing system, until a new board is delivered. The delivery time, Y, is uniformly distributed on the interval two to six days. The cost of a board failure and interruption includes the fixed cost c0 of a new board and a cost that increases proportionally to Y2. If C is the cost incurred, C = c0 + c1Y2.
A) Find the probability that the delivery time exceeds two days.
B) In terms of c0 and c1, find the expected cost associated with a single failed circuit board.

Answers

Answer:

a) 1  ( 100% )

b)   Co + 46/3 C1

Step-by-step explanation:

Delivery time = Y

Interval = 2 to 6 days

cost incurred ( C ) = Co + C1 Y^2

a) determine the probability that the delivery time exceeds two days

since the delivery time is uniformly distributed on the interval 2 to 6 days the probability of having a delivery time > 2 days will be = 1

b) Determine the expected cost associated with a single failed circuit board

E ( Y^2 ) = 46/3

hence the cost associated with a single failed circuit board =

E ( C ) = Co + 46/3 C1

attached below is a detailed solution

Heating and cooling bills will be about ​% less than in a similar​ wood-framed building in upstate New York. An ICF home will be approximately ​% more expensive to construct than a​ wood-framed home. For a typical ft home costing ​$ ft to construct in upstate New York and costing ​$ per month to heat and​ cool, how many months does it take for a ft ICF home to pay back its extra construction​ cost?

Answers

Complete question :

Insulated concrete forms​ (ICF) can be used as a substitute for conventional wood framing in building construction. Heating and cooling bills will be about 60​% less than in a similar​ wood-framed building in upstate New York. An ICF home will be approximately 10​% more expensive to construct than a​ wood-framed home. For a typical 1,800 ftsquared2 home costing ​$130 ftsquared2 to construct in upstate New York and costing ​$260 per month to heat and​ cool, how many months does it take for a 1,800 ftsquared2 ICF home to pay back its extra construction​ cost?

Answer:

150 months

Step-by-step explanation:

Wood framing Construction cost :

Cost per ft² = $130

Total cost for 1800 ft² :

1800 * $130 = $234,000

Heating and cooling cost = $260

An ICF home:

Construction cost will be approximately 10% more expensive :

Hence, total cost of ICF = (1.1) * 234000 = $257,400

Extra cost on construction :

$257,400 - $234000 = $23,400

Heating and cooling cost ; 60% less expensive = (1 - 0.6) * $260 = $104

Saving in heating and cooling = $260 - $104 = $156 monthly

Number of months it takes to pay extra cost on construction :

Extra cost on construction / saving in heating & cooling

= $23,400 / $156

= 150 months

A jar contained 8 balls: 6 red, 1 green and 1 blue. We randomly take a ball out of the jar. Once a ball is selected we do not put it back. We keep selecting balls until for the first time we get a blue one. We count the number of times we had to draw a ball, (including the last drawing) until we actually got the blue ball. How many elements are in the sample space for this experiment

Answers

Answer:

35

Step-by-step explanation:

Given that :

Number of balls = 8

Red (R) = 6 ; 1 green(G) ; 1 BLUE (B)

Possibilities unt a blue ball is picked :

B, RB, GB, RRB, RGB, GRB, G

Draw 1 = B = 1

Draw 2 = B = 2C1 = 2

Draw 3 = B = 3C2 = 3

Draw 4 = B = 3C3 + 3C1 = 1 + 3 = 4

Draw 5 = B = 4C4 + 4C1 = 1 + 4 = 5

Draw 6 = B = 5C5 + 5C1 = 1 + 5 = 6

Draw 7 = B = 6C6 + 6C1 = 1 + 6 = 7

Draw 8 = B = 6C6 + 6C1 = 1 + 6 = 7

Taking the sum:

(1 + 2 + 3 + 4 + 5 + 6 + 7 + 7) = 35

There are 35 elements in the sample space

Compute 292,000 divide 100

Answers

Answer:

Step-by-step explanation:

is pretty simple

292,000/100=2,920

BONJOUR asker

Answer:

2920

Step-by-step explanation:

292000 divided by 100 is 2920

#CarryOnLearning

heyoitzmeh from Philippines

you can foIlow me in my brainly in Philippines

Need help don’t know what to do I’m confused

Answers

Im pretty sure it’s D. Y= 0.5x + 3 :)

2. The ratio of pretzels to peanuts in a trail mix is 4:9.
At the same rate if there are 80 pretzels how many
peanuts are there?

Answers

Answer:

170 peanuts I believe

Step-by-step explanation:

just did mental math, not sure if it's the right way

Can someone please explain this!
(-5x^2+3)-(-x^3+9x^2+9)

Answers

9514 1404 393

Answer:

  x^3 -14x^2 -6

Step-by-step explanation:

Your expression is the difference of two polynomials. The parentheses can be removed by using the distributive property. The minus sign outside the second set of parentheses applies to each term inside parentheses.

  -5x^2 +3 +x^3 -9x^2 -9

Now, you can group like terms. In "standard form", the degrees of the terms decrease from left to right.

  x^3 +(-5x^2 -9x^2) +(3 -9)

And combine like terms.

  x^3 -14x^2 -6 . . . . . simplified form of the given expression

Congruent and similar figures need help I’ll cash app anyone who does my math work $10 for 2 assignments

Answers

First part:
Angle A ≅ Angle T
Angle C ≅ Angle R
Angle D ≅ Angle U
AB ≅ TS
DA ≅ TU
ST ≅ BA

Find the perimeter of the figure to the nearest tenth of a centimeter.

2 points

Answers

90918 is the answer

Which expression is equivalent to -2v​+(​-4)+8​+(-​3v)?

Answers

Answer:

5v+4

Step-by-step explanation:

-90 = -100 + x help need answer

Answers

Answer:

10 =x

Step-by-step explanation:

-90 = -100 + x

Add 100 to each side to isolate x

-90+100 = -100+100 + x

10 =x

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