A particle moves along the x-axis. The velocity of the particle at time t is −2t+8 . What is the total distance traveled by the particle from t=1 to t=6?

Answers

Answer 1

Answer:

13

Step-by-step explanation:

The velocity is given by:

[tex]\displaystyle v(t)= -2t + 8[/tex]

And the total distance given the velocity is given by:

[tex]\displaystyle \int_{a}^{b}|v(t)|\, dt[/tex]

So, the total distance traveled by the particle from t = 1 to t = 6 will be:

[tex]\displaystyle d=\int_{1}^{6}|-2t+8|\, dt[/tex]

The absolute value tells us that:

[tex]\displaystyle |-2t+8| = \left\{ \begin{array}{ll} -2t+8 & \quad x \leq 4 \\ -(-2t+8) & \quad x > 4\\ \end{array} \right[/tex]

So, split the integral into two parts:

[tex]\displaystyle d=\int_{1}^{4} (-2t+8)\, dt+\int_{4}^{6}(-(-2t+8))\, dt[/tex]

Integrate:

[tex]\displaystyle d=(-t^2+8t)\Big|_{1}^{4}+(t^2-8t)\Big|_{4}^{6}[/tex]

Evaluate:

[tex]\begin{aligned} d&=[(-4^2+8(4))-(-1^2+8)]+[(6^2-8(6))-(4^2-8(4)]\\ &= [16-7]+[-12-(-16)]\\ &=9+4 \\ &=13 \end{aligned}[/tex]


Related Questions

The perimeter of a triangle is 38 feet. One side of the triangle is 4 feet shorter than the second side. The third side is 6 feet longer than the second side. Find the length of each side.

Answers

Answer:

First side, a = 8 ft.

Second side = 12 ft.

Third side, c = 18 ft.

Step-by-step explanation:

Let the sides of the triangle be a, b and c respectively.

Given the following data;

Perimeter = 38ft

First side, a = b - 4

Third side, c = b + 4

The perimeter of a triangle is given by the addition of all its three (3) sides.

Mathematically, the perimeter of a triangle is given by the formula;

P = a + b + c

Substituting into the equation, we have;

38 = (b - 4) + b + (b + 6)

38 = 3b + 2

3b = 38 - 2

3b = 36

b = 36/3

b = 12ft

To find the first side, a;

a = b - 4

a = 12 - 4

a = 8ft.

To find the third side, c

c = b + 6

c = 12 + 6

c = 18 ft.

question 1 a physician’s “patient panel” is the list of all patients under their care. in the us, the size of patient panels among primary care doctors is well modeled by a n (1500, 200) distribution. (a) draw a normal curve for this model, labeling the empirical rule (68-95-99.7 rule). (b) if a “medium-sized” panel has anywhere from 1100 to 1700 patients, what proportion of us primary care doctors have a patient panel that is not “medium-sized”? (c) find q1,q3 and the iqr for this distribution.

Answers

Answer:

sorry but i really do’t know

Sam weighs 51 kg what is the weigh to the nearest stone ?use the conversion 1kg=2.2 pound and 14 pounds = 1 stone

Answers

Answer:

8/14

Step-by-step explanation:

51 kg

51 x 2.2 =112.2

112.2/14 =8.014 ≈ 8

8/14

The function f(x) =5x coverts x nickels to pennies. Find a function that converts X Pennys to Nichols then convert 50 pennies to Nichols. 

Answers

Answer:

[tex]f'(x) = \frac{1}{5}x[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x[/tex] --- Nickel to Penny

Required

Determine the function that converts penny to nickel

This question implies that we determine the inverse of the function.

We have:

[tex]f(x) = 5x[/tex]

Represent f(x) with y

[tex]y = 5x[/tex]

Swap the positions of x and y

[tex]x = 5y[/tex]

Make y the subject by dividing both sides by 5

[tex]\frac{1}{5}x = \frac{5y}{5}[/tex]

[tex]\frac{1}{5}x = y[/tex]

[tex]y =\frac{1}{5}x[/tex]

Replace y with f'(x)

[tex]f'(x) = \frac{1}{5}x[/tex]

Hence, the function that converts x pennies to nickels is [tex]f'(x) = \frac{1}{5}x[/tex]

Students in a reading class have three options for their book project: making a brochure, writing a news article, or designing a computer presentation.

Answers

The correct answer is:
- brochure 4 blue chips
- article 6 yellow chips
- computer presentation 10 red chips

Work: you have to do the proportions
• 20 : 100= x : 20 ➡️ (20 • 20): 100= 4
• 30 : 100 = x : 20 ➡️ (30 • 20):100= 6
• 50 : 100 = x : 20 ➡️ (50 • 20) : 100: 10

Proof:
4 + 6 + 10= 20 chips

Answer:

4

6

10

Please give me brainliest, I really need it.

Find the volume of the rectangular prism. 4 in 3 [in 4 in 4 in​

Answers

Answer:

12

Step-by-step explanation:

what is Pythagorean triples​

Answers


A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.

Answer:

A pythagorean triplet is a set of three numbers  which satisfies the pythagoreus theorum - ( a^2+b^2=c^2).

Example:

3, 4 and 5

3^2 + 4^2 = 5^2

9+ 16 = 25

I hope am right!

Find the slope of the line through the given pair of points.
(0, -19), (20, 15)

Answers

Answer:

M = 17/10

Step-by-step explanation:

Question 11

Select all expressions that are equivalent to 9(6k + 3r).

A

15k + 121

B

54k + 27r

С

6(3k + Or)

D

3(18k +91)

Answers

Answer:

I think it is d

Step-by-step explanation:

so sorry if it wrong i tried my best

Answer:

b for sure im not sure if there are any more

ugh i have this question and im not sure if there are any other answers

Step-by-step explanation:

Explain 5 different ways you use Math in your everyday life.
This is a telpas thing btw

Answers

Answer:

School, Looking at what episode of anime I am on, Looking at the time, Looking at my calendar, and another is when I am doing brain teasers!

Step-by-step explanation:

Does this count?

Answer:

Time deltas

Step-by-step explanation:

help me please:) will very much appreciate it

Answers

1. 18
2. 7/4

Here is my answer, hope to help you

A civil servant had a salary of Rs. 9600. Tax up to
Rs. 85000 per year would be exempted. If he paid
Rs. 377.50 as a tax per month, how much percent of
tax was imposed ?
(Ans: 15 %​

Answers

Answer:

Step-by-step explanation:

The question is misleading. It was not specified that his salary is Rs 9,600 per month. That is 115,200 yearly. Of that, 115,200- 85,000 = 30,200 is taxable.

tax = Rs 377.50/month = Rs 4,530/year

4,530/30,200 = 0.15 = 15%

Jayden kept track of the number of hours that she spent
playing softball each week for several weeks. She spent 4,
7,3, and 6 hours.
What is the mean number of hours that Jayden spent playing softball each
week?
A. 20 hours
B. 5 hours
C. 7 hours
D. 4 hours

Answers

The answer is 20 because you add all the numbers

Answer:

The answer is 5

Step-by-step explanation:

Nathan is going to invest in an account paying an interest rate of 6% compounded continuously. How much would Nathan need to invest, to the nearest ten dollars, for the value of the account to reach $1,200 in 8 years?

Answers

Answer:

731.48

Step-by-step explanation:

you take 6 percent form 100 percent with give 94 percent

then you times 1200 by 94 percent 8 times to get awnser

Answer:700

Step-by-step explanation:

Jada’s teacher fills a travel bag with 5 copies of a textbook. The weight of the bag and books is 17 pounds. The empty travel bag weighs 3 pounds. How much does each book weigh? whats the equation not the answer

Answers

5×3=15

17+15=32

Step-by-step explanation:

3÷17=15

15+5=20

Answer:

Step-by-step explanation:

can someone please help me with this. i will give you brainliest

Answers

Answer: I want to say it is the second one, but i'm not to sure.

Step-by-step explanation:

I think it would be the second one!

What are the coordinates of the image of point T(2,4) over the transformation D(1/2,R), where R(6,-2) is the center. X= ? Y= ?

Answers

9514 1404 393

Answer:

  T'(4, 1)

Step-by-step explanation:

The dilation transformation around a center not the origin is ...

  T' = k(T -R) +R . . . . for dilation factor k and center R

This can be simplified to ...

  T' = 1/2T -1/2R +R = 1/2T +1/2R = (T +R)/2

Using the given point values, we find the image point to be ...

  T' = ((2, 4) +(6, -2))/2 = (8, 2)/2 = (4, 1)

The image point is T'(4, 1).

What can be said about a set of data with a standard deviation of​ 0? ​(This is a reading assessment question. Be certain of your answer because you only get one attempt on this​ question.) Choose the correct answer below. A. All the observations are the same value. B. All the observations are 0. C. For every positive​ value, there is a corresponding negative value​ (as in 4 and −​4; 6 and −​6).

Answers

Answer:

A.) All the observations are the same value

Step-by-step explanation:

One of the statistical measures used to determine the spread or variability of a dataset is the variance or standard deviation. The standard deviation determines how a set of value varies about the mean value.

Mathematically,

Variability or spread = mean + number of standard deviations

Hence, a standard deviation of 0 ; means they there is no variability in the dataset. Hence, a standard deviation of 0 means all observations are of the same value.

For a set of data with a standard deviation of 0, the correct option is:

A: "All the observations are the same value."

What is the standard deviation?

For a given set {x₁, x₂, ...} with N elements.

With a mean M, we define the standard deviation as:

[tex]S= \sqrt{\frac{\sum (x_i - M)^2}{N - 1} }[/tex]

Notice that, because we have a squared element in the sum, all the elements of the sum are positive. So if we have a single value of the set that is different than the mean, then the standard deviation will be larger than zero.

Then the only case where the standard deviation is zero is the case where all the elements of the set are equal to the mean of the set, and that only happens if all the elements of the set are equal.

So the correct option is A:

"All the observations are the same value. "

If you want to learn more about standard deviation, you can read:

https://brainly.com/question/15858152

f(x) =
=
Find f'(x) and f''(x).
+
EL
ALEHER
24
) (
f''(x) = {
Epe

Answers

To make things easier, first rewrite

f(x) = x / (x + 7/x) = x ² / (x ² + 7)

i.e. multiply f by x/x, which is valid because x can't be 0 anyway as it's outside the domain of f.

Now, by the quotient and chain rules, we get

f '(x) = ((x ² + 7) (x ²)' - x ² (x ² + 7)') / (x ² + 7)²

… = (2x (x ² + 7) - x ² (2x)) / (x ² + 7)²

… = (2x ³ + 14x - 2x ³) / (x ² + 7)²

… = 14x / (x ² + 7)²

f ''(x) = ((x ² + 7)² (14x)' - (14x) ((x ² + 7)²)') / ((x ² + 7)²)²

… = (14 (x ² + 7)² - (14x) (2 (x ² + 7)² (x ² + 7)')) / (x ² + 7)⁴

… = (14 (x ² + 7)² - (14x) (2 (2x) (x ² + 7)²)) / (x ² + 7)⁴

… = (14 (x ² + 7)² - 4x (14x) (x ² + 7)²) / (x ² + 7)⁴

… = 14 (x ² + 7)² (1 - 4x) / (x ² + 7)⁴

… = 14 (1 - 4x) / (x ² + 7)²

… = (14 - 56x) / (x ² + 7)²

an aquarium has a length of 7/2 feet, a width of 4/3 feet and a height of 3/2 feet. what is the volume of the aquariam

Answers

Answer:

7

Step-by-step explanation:

V = l x w x h

=7/2 x 4/3 x 3/2

=84/12

=7 feet cubed

Y= 2/3x + 2. Y= 3/5x + 3. Graph equations

Answers

One square = 1 unit

Answers are on paper.
I put them on separate graph

A soccer team gets three points for a win, one point for a tie, and zero points for a loss. The team plays ten games and has three more wins than losses. What is the greatest possible number of points the team could have?

Answers

Answer: 19.

Step-by-step explanation:

The highest you can go is 6 and 3 because you can't do 7 and 4. 6 wins would add up to 18 points. The one game that is missing we can say could be a tie, which would add 1 point, making it 19 possible points.

Answer:

Highest number of wins and losses can only be 6 & 3 and if u take 7 & 4 as taking 7&4 will make total 11 and we know that there was only 10 games.

So we can conclude like this

Number of wins: 6

Number of losses: 3

Number of draws: 1

Thus the points will be, (6*3)+(3*0)+(1*1)

18+0+1

=19 points

Helpppppppp with Tuesday question 1 pleaseeeeeee

Answers

Answer:

k = 2.8

Step-by-step explanation:

Subtract 3.9 from both sides of the equation

k + 3.9 = 6.7

k + 3.9 - 3.9 = 6.7 - 3.9

k = 3.9 - 6.7

k = 2.8

PLS HELP!!

The corresponding sides of triangles ABC and DEF are congruent. Which statements are always true for triangles ABC and DEF? Select all that apply.

A.) There is a sequence of rigid motions that carries ABC to triangle DEF.
B.) triangles ABC and DEF are congruent by side-side-side.
C.) triangles ABC and DEF are both equilateral triangle‘s by side-side-side.

Answers

Answer:

A and B are true

Step-by-step explanation:

Write the equation of the line of reflection in the following picture

Answers

Answer:

it is reflected in the x-axis so y=0

When Sam's little brother was born, he was 18 inches tall. Each year, he grows an average of 3 inches.

Answers

Y=18 +3x should be the equation

Is 0.88 bigger or smaller or equal to 0.178

Answers

.88 is greater than .178

hope i helped !

Answer:

0.88 is bigger than 0.178

Step-by-step explanation:

0.8 > 0.1

So you can assume 0.88 is bigger than 0.178

Weak battery is considered to be a part of routine
O A. wear and tear
O B. maintenance
O C. check
O D. inspection

Answers

Answer:

A. wear and tear

Step-by-step explanation:

A battery is generally expected to become weaker over time, as a consequence of the normal use of equipment. The presence of a weak battery would be found by a routine check, and replaced by routine maintenance.

The fact that a battery is weak would be considered the result of routine wear and tear

Round the number 3,454,877 to the nearest 100,000.*

Answers

Answer:

3,500,000

Step-by-step explanation:

the ten thousands place is a 5 so you round the 4 up to a 5

simplify
square roots.

Answers

Answer:

zy^5

Step-by-step explanation:

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