CALCULUS: For an object whose velocity in ft/sec is given by v(t) = sin(t), what is its distance, in feet, travelled on the interval t = 1 to t = 5?
A. 0.45
B. 2.82
C. 0.03

Answers

Answer 1

The linked answer is wrong because that integral gives you the net displacement of the object, not the total distance.

To get the distance, you have to integrate the speed (as opposed to velocity), which involves integrating the absolute value of the velocity function.

[tex]\mathrm{distance} = \displaystyle\int_1^5 |\sin(t)| \,\mathrm dt[/tex]

By definition of absolute value,

[tex]|\sin(t)|=\begin{cases}\sin(t)&\text{for }\sin(t)\ge0\\-\sin(t)&\text{for }\sin(t)<0\end{cases}[/tex]

Over this particular integration interval,

• sin(t ) ≥ 0 for 1 ≤ tπ, and

• sin(t ) < 0 for π < t ≤ 5

so you end up splitting the integral at t = π as

[tex]\mathrm{distance} = \displaystyle\int_1^\pi \sin(t)\,\mathrm dt + \int_\pi^5 (-\sin(t))\,\mathrm dt[/tex]

Now compute the distance:

[tex]\mathrm{distance} = -\cos(t)\bigg|_1^\pi + \cos(t)\bigg|_\pi^5[/tex]

[tex]\mathrm{distance} = -(\cos(\pi) - \cos(1)) + (\cos(5) - \cos(\pi))[/tex]

[tex]\mathrm{distance} = -2\cos(\pi) + \cos(1) + \cos(5) \approx 2.82[/tex]

making B the correct answer.


Related Questions

The number of bacteria in a certain population increases according to a continuous exponential
growth model at a rate of 8.1% per hour. There are 1800 bacteria at t = 0.
Write an equation that gives the number of bacteria after t hours.

Answers

Answer:

Step-by-step explanation:

Let p: The kitchen is clean.
Let q: The bedroom is clean.
Which statement iS true if the kitchen is clean but the bedroom is not clean?
• If p is true, then q is true.
• Statement q if is true if and only if p is true.
• Both p and q are true.
• Statement p or q is true.

Answers

Answer:

the last one would be the answer as we know the kitchen is clean so it might be some if true

.
What is cot(A)?
0 37
7
3,2
7
O 37
O 32
7
0 31

Answers

Answer:

may I see a photo?

Step-by-step explanation:

Answer:

its A -3 (squareroot of 7)/7

Step-by-step explanation:

HL criteria of congruence can be used only with?

Answers

Answer: Right triangles or a hypotenuse and a leg


PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.

Answers

Answer:

Step-by-step explanation:

(1, 72) (2, 73)

(73 - 72)/(2 - 1)= 1/1= 1

y - 72 = x - 1

y = x + 71

Happy valentines dayyyy math suckss help pleaseeeeeee

Answers

Happy Valentine’s Day and the answer is number 3

Write the expression with a factor of -1.

-3y
-x-y
-6+5b
3-8m

Answers

15b + 22ym = 15 is the answer

HELP ME DO THIS PROBLEM PLEASE PLEASE

Answers

Answer:

p=1

Step-by-step explanation:

5p=p+4

5p-p=4

4p=4

p=1

5p=5×1=5

p+4=1+4=5

p+16=1+16=17

17p=17×1=17

You have a bid of $250 per room for 180 guest rooms. You want to comp 12 rooms for the upcoming teacher convention. What is your average room rate across the paid and free rooms? Round to the nearest dollar.

a) $234
b) $244
c) $250
d) $254

Answers

Answer:

C

Step-by-step explanation:


I’m confused, any help?

Answers

Answer:

D

Step-by-step explanation:

Trust me its D because to equal f(x)--->Inf., you need to have x equal a negative

D hope this helps your welcome

what is 5/9 + 1/3? (please show your work)

Answers

Answer:

8/9

Step-by-step explanation:

First: Turn the 1/3 in 3/9 (You have to find the common denonminator or bottom number in a fraction)

Second: add (3/9 + 5/9= 8/9)

Answer: 8/9

(Brainliest??)

The value of the fractional expression 5/9 - 1/3 will be 17 / 3.

What is Algebra?

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

5/9 and 1/3

Then the difference between the numbers 5/9 and 1/3 will be given by putting a minus sign between them. Then we have

⇒ 5/9 - 1/3

⇒ (5 - 3) / 9

⇒ 2 / 9

The value of the fractional expression 5/9 - 1/3 will be 17 / 3.

More about the Algebra link is given below.

https://brainly.com/question/953809

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Ben just walked into Best Buy and saw the TV of his
dreams! It's a 60 inch 4K Smart TV that is on sale for
$550. What a bargain! How much will Ben have to pay in
tax (MA sales tax is 6.25%)?
Be sure to LABEL your answer!
(Note: with sales tax problems, you may need to round
your answer to the nearest penny.)

Answers

Answer:

$6.30

Step-by-step explanation:

Given the expression 2(3x + 1), what would be the resulting equivalent expression after the distributive property is applied?

Answers

Answer:

6x + 2

Step-by-step explanation:

2(3x + 1)

Multiply 2 with 3x and 1.

6x + 2

Answer:

6x + 2

Step-by-step explanation:

2 x 3= 6

2 x 1= 2

I really need help omgggggggg

Answers

Answer:

The 3rd one  Abc is a congeuent

A comedian is planning to make his show more appealing by telling three jokes at the beginning of each show. He has been booked in a bar for the next three months. If he gives one performance a night, and he never wants to repeat the same set of jokes on any two nights, what is the minimum number of jokes he needs to prepare?

Answers

Answer:

135 jokes

Step-by-step explanation:

3 months = 90 days

90/2 = 45 days of new jokes

45 days x 3 jokes per day = 135 jokes

ASAP: #43. Find the area of triangle ABC given A = 42.5°, b = 13.6, c = 10.1 (Draw a triangle, give answer to nearest tenth!)

Correct answer gets marked brainliest:)

Answers

Answer:

The area of a triangle  A = 46.399 square units

Step-by-step explanation:

Explanation:-

Given that ΔABC

Given ∠ A = 42.5° and sides b= 13.6 and c =10.1

The area of a triangle

                [tex]A = \frac{1}{2} b c sin A[/tex]

                [tex]A = \frac{1}{2} 13.6(10.1) sin 42.5[/tex]

                [tex]A = \frac{1}{2} 137.36(0.67559)[/tex]         (∵ sin (42.5)° = 0.67559

               A = 46.399 square units

Find all real zeros of the function y=-9x-1
A. -9
B. 1/-9
C. 1/9
D. -9 -1
Please select the best answer from the choices proided

Answers

Answer:

OPTION D

Explanation:

For zeros of the function (y is the function, a function of x) we need y = 0 so that in turn means we need - 9x - 1 = 0 or - 9x = 1 (i.e. add 1 to both sides); now divide by - 9, and x = 1/-9 which is exactly the same as - 1/9 or - (1/9) and this is the only zero of the function.

or

If y = -9x - 1,

When y = 0

0 = -9x - 1

0 + 1 = -9x - 1 + 1

1 = -9x

1/9 = -9x/9

1/9 = -x

1/[9 X (-1)] = -x/-1

- (1/9) = x

When x = 0

y = (-9 X 0) - 1

y = 0 - 1

y = - 1

Question 7
Laura had 23 ounces of plant food. She wants to use the same amount of plant food each day on her garden. She wants to use all the plant food she has before buying more. Which statement is true?
If she uses plant food in her garden for 6 days, she uses
1
6
ounces of plant food each day
B
2
If she uses plant food in her garden for 10 days, she uses 2
23
ounces of plant food each day
Ounces of plant food each day
С
If she uses plant food in her garden for 8 days, she uses 3
8
8
1
D
If she uses plant food in het garden for 11 days, she uses 2 11 ounces of plant food each day

Answers

Answer:

(d) and (e) are true

Step-by-step explanation:

Given

[tex]Food = 23\ oz[/tex]

See attachment for proper presentation of question

Required

Select all true statements

For any option to be true, it must satisfy the following condition.

[tex]Days * Food = 23[/tex]

Option (a):

[tex]Days = 6[/tex]

[tex]Food = 4\frac{1}{6}[/tex] per day

So, we have:

[tex]Days * Food = 6 * 4\frac{1}{6}[/tex]

[tex]Days * Food = 6 * \frac{25}{6}[/tex]

[tex]Days * Food = 25[/tex]

This is not true because: [tex]25 \ne 23[/tex]

Option (b):

[tex]Days = 10[/tex]

[tex]Food = 2\frac{2}{23}[/tex] per day

So, we have:

[tex]Days * Food = 10 * 2\frac{2}{23}[/tex]

[tex]Days * Food = 10 * \frac{48}{23}[/tex]

[tex]Days * Food = \frac{480}{23}[/tex]

[tex]Days * Food = 21[/tex] --- approximated

This is not true because: [tex]21 \ne 23[/tex]

Option (c):

[tex]Days = 8[/tex]

[tex]Food = 3\frac{1}{8}[/tex] per day

So, we have:

[tex]Days * Food = 8 * 3\frac{1}{8}[/tex]

[tex]Days * Food = 8 * \frac{25}{8}[/tex]

[tex]Days * Food = 25[/tex] --- approximated

This is not true because: [tex]25 \ne 23[/tex]

Option (d):

[tex]Days = 11[/tex]

[tex]Food = 2\frac{1}{11}[/tex] per day

So, we have:

[tex]Days * Food = 11 * 2\frac{1}{11}[/tex]

[tex]Days * Food = 11 * \frac{23}{11}[/tex]

[tex]Days * Food = 23[/tex] --- approximated

This is true because: [tex]23 = 23[/tex]

Option (e):

[tex]Days = 7[/tex]

[tex]Food = 3\frac{2}{7}[/tex] per day

So, we have:

[tex]Days * Food = 7 * 3\frac{2}{7}[/tex]

[tex]Days * Food = 7 * \frac{23}{7}[/tex]

[tex]Days * Food = 23[/tex] --- approximated

This is true because: [tex]23 = 23[/tex]

List 3 values that would make this inequality true.

Answers

Answer: n < 2, n < 1

Step-by-step explanation:

Find the Width of the Rectangular Prism.

Answers

Answer:

w = V/12 IN X= 840in then 840÷12 = 70in

A rectangular prism has 70in width having volume 840in³, length is 2in, and height 6in.

What is a rectangular prism?

A rectangular prism or a  cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

V = (l×w×h).

The total surface area of a cuboid is 2( lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, A rectangular prism has a volume 840 in³, its length is 2 in and its height is 6in.

Assuming width to be w in.

∴ (l×w×h) = volume.

(2×w×6) = 840.

12w = 840.

w = 70 in.

learn more about cuboid here :

https://brainly.com/question/19754639

#SPJ2

5.2 × _______ = 5.2 whats the answer

Answers

Answer:

1

Step-by-step explanation:

question 1: Multiply and simplify.

x^2⋅x⋅x^5
(I got x^8 but I was unsure.)

question 2: Multiply and simplify.

(3x+7)8x^2

Answers

Answer:

question 1 = x7 and question 2 = 24x^3+56x^2 I'm pretty sure

Which sentence is true?

Answers

Answer:

B

Step-by-step explanation:

box there are 10 blue marbles for every 35 red marbles what is the reduced ratio of red marbles : blue marbles​

Answers

10:35, both are divisible by 5
2:7

PLEASE HELP I NEED THE ANSWER NOW WILL GIVE YOU BRAINLEST

Answers

Answer:

your answer is C

Step-by-step explanation:

Answer:

D. x>8

Step-by-step explanation:

I NEED HELP WITH THIS​

Answers

Answer:

its A and C and D

Step-by-step explanation:

The radius of a circle is 3 yards. What is the circle's circumference?​

Answers

Answer:

18.85

Step-by-step explanation:

2(3.14)(3)

write a congruence statement for the figures below . pleeasse show your work ​

Answers

Answer:

[tex] \triangle FDE \cong \triangle RTS[/tex]

Step-by-step explanation:

[tex] In \:\triangle FDE \:\&\:\triangle RTS[/tex]

[tex] FD \cong RT... (given) [/tex]

[tex] \angle FDE \cong \angle RTS... (given)[/tex]

[tex] DE \cong TS... (given) [/tex]

[tex] \therefore \triangle FDE \cong \triangle RTS\\(by\: SAS\: postulate)[/tex]

The sum of 4 consecutive odd integers is 40. Find the first number algebraically.

Answers

Step-by-step explanation:

2n+1+2n+3+2n+5+2n+7

8n+16=40

8n=40-16

8n=24

n=3

Warmup 2/16/21(create a table to compare the 2)
.
If you were babysitting, would you rather
Charge $5 for the first hour and $8 for each additional
hour?
bry
SY
.
Or
Charge $15 for the first hour and $6 for each additional
hour?
ebo...
Explain your reasoning.
ng

Answers

The 1st one because you get more money out of it
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