Answers
2) the third option
hope this helped!
Answer:
1) 2/x³ the secound option
2)1/x²⁴ the secound option
I think
Related Questions
The function v(t) is the velocity in m/sec of a particle moving along the x-axis. Use analytic methods to do each of the following: (a) Determine when the particle is moving to the right, to the left, and stopped. (b) Find the particle's displacement for the given time interval. If s(0) = 3, what is the particle's final position? (c) Find the total distance traveled by the particle. v(t) = 5 (sint)^2(cost); 0 ≤ t ≤ 2π
Answers
Answer:
(a) The particle is moving to the right in the interval [tex](0 \ , \ \displaystyle\frac{\pi}{2}) \ \cup \ (\displaystyle\frac{3\pi}{2} \ , \ 2\pi)[/tex] , to the left in the interval [tex](\displaystyle\frac{\pi}{2}\ , \ \displaystyle\frac{3\pi}{2})[/tex], and stops when t = 0, [tex]\displaystyle\frac{\pi}{2}[/tex], [tex]\displaystyle\frac{3\pi}{2}[/tex] and [tex]2\pi[/tex].
(b) The equation of the particle's displacement is [tex]\mathrm{s(t)} \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ 3[/tex]; Final position of the particle [tex]\mathrm{s(2\pi)} \ = \ 3[/tex].
(c) The total distance traveled by the particle is 9.67 (2 d.p.)
Step-by-step explanation:
(a) The particle is moving towards the right direction when v(t) > 0 and to the left direction when v(t) < 0. It stops when v(t) = 0 (no velocity).
Situation 1: When the particle stops.
[tex]\-\hspace{1.7cm} v(t) \ = \ 0 \\ \\ 5 \ \mathrm{sin^{2}(t)} \ \mathrm{cos(t)} \ = \ 0 \\ \\ \-\hspace{0.3cm} \mathrm{sin^{2}(t) \ cos(t)} \ = \ 0 \\ \\ \mathrm{sin^{2}(t)} \ = \ 0 \ \ \ \mathrm{or} \ \ \ \mathrm{cos(t)} \ = \ 0 \\ \\ \-\hspace{0.85cm} t \ = \ 0, \ \displaystyle\frac{\pi}{2}, \ \displaystyle\frac{3\pi}{2} \ \ \mathrm{and} \ \ 2\pi[/tex].
Situation 2: When the particle moves to the right.
[tex]\-\hspace{1.67cm} v(t) \ > \ 0 \\ \\ 5 \ \mathrm{sin^2(t) \ cos(t)} \ > \ 0[/tex]
Since the term [tex]5 \ \mathrm{sin^{2}(t)}[/tex] is always positive for all value of t of the interval [tex]0 \ \leq \mathrm{t} \leq \ 2\pi[/tex], hence the determining factor is cos(t). Then, the question becomes of when is cos(t) positive? The term cos(t) is positive in the first and third quadrant or when [tex]\mathrm{t} \ \epsilon \ (0, \ \displaystyle\frac{\pi}{2}) \ \cup \ (\displaystyle\frac{3\pi}{2}, \ 2\pi)[/tex] .
*Note that parentheses are used to demonstrate the interval of t in which cos(t) is strictly positive, implying that the endpoints of the interval are non-inclusive for the set of values for t.
Situation 3: When the particle moves to the left.
[tex]\-\hspace{1.67cm} v(t) \ < \ 0 \\ \\ 5 \ \mathrm{sin^2(t) \ cos(t)} \ < \ 0[/tex]
Similarly, the term [tex]5 \ \mathrm{sin^{2}(t)}[/tex] is always positive for all value of t of the interval [tex]0 \ \leq \mathrm{t} \leq \ 2\pi[/tex], hence the determining factor is cos(t). Then, the question becomes of when is cos(t) positive? The term cos(t) is negative in the second and third quadrant or [tex]\mathrm{t} \ \epsilon \ (\displaystyle\frac{\pi}{2}, \ \displaystyle\frac{3\pi}{2})[/tex].
(b) The equation of the particle's displacement can be evaluated by integrating the equation of the particle's velocity.
[tex]s(t) \ = \ \displaystyle\int\ {5 \ \mathrm{sin^{2}(t) \ cos(t)}} \, dx \ \\ \\ \-\hspace{0.69cm} = \ 5 \ \displaystyle\int\ \mathrm{sin^{2}(t) \ cos(t)} \, dx[/tex]
To integrate the expression [tex]\mathrm{sin^{2}(t) \ cos(t)}[/tex], u-substitution is performed where
[tex]u \ = \ \mathrm{sin(t)} \ , \ \ du \ = \ \mathrm{cos(t)} \, dx[/tex].
[tex]s(t) \ = \ 5 \ \displaystyle\int\ \mathrm{sin^{2}(t) \ cos(t)} \, dx \\ \\ \-\hspace{0.7cm} = \ 5 \ \displaystyle\int\ \ \mathrm{sin^{2}(t)} \, du \\ \\ \-\hspace{0.7cm} = \ 5 \ \displaystyle\int\ \ u^{2} \, du \\ \\ \-\hspace{0.7cm} = \ \displaystyle\frac{5u^{3}}{3} \ + \ C \\ \\ \-\hspace{0.7cm} = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ C \\ \\ s(0) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(0)} \ + \ C \\ \\ \-\hspace{0.48cm} 3 \ = \ 0 \ + \ C \\ \\ \-\hspace{0.4cm} C \ = \ 3.[/tex]
Therefore, [tex]s(t) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ 3[/tex].
The final position of the particle is [tex]s(2\pi) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(2\pi)} \ + \ 3 \ = \ 3[/tex].
(c)
[tex]s(\displaystyle\frac{\pi}{2}) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(\frac{\pi}{2})} \ + \ 3 \\ \\ \-\hspace{0.85cm} \ = \ \displaystyle\frac{14}{3} \qquad (\mathrm{The \ distance \ traveled \ initially \ when \ moving \ to \ the \ right})[/tex]
[tex]|s(\displaystyle\frac{3\pi}{2}) - s(\displatstyle\frac{\pi}{2})| \ = \ |\displaystyle\frac{5}{3} \ (\mathrm{sin^{3}(\frac{3\pi}{2})} \ - \ \mathrm{sin^{3}(\displaystyle\frac{\pi}{2})})| \ \\ \\ \-\hspace{2.28cm} \ = \ \displaystyle\frac{5}{3} | (-1) \ - \ 1| \\ \\ \-\hspace{2.42cm} = \displaystyle\frac{10}{3} \\ \\ (\mathrm{The \ distance \ traveled \ when \ moving \ to \ the \ left})[/tex]
[tex]|s(2\pi) - s(\displaystyle\frac{3\pi}{2})| \ = \ |\displaystyle\frac{5}{3} \ (\mathrm{sin^{3}(2\pi})} \ - \ \mathrm{sin^{3}(\displaystyle\frac{3\pi}{2})})| \ \\ \\ \-\hspace{2.28cm} \ = \ \displaystyle\frac{5}{3} | 0 \ - \ 1| \\ \\ \-\hspace{2.42cm} = \displaystyle\frac{5}{3} \\ \\ (\mathrm{The \ distance \ traveled \ finally \ when \ moving \ to \ the \ right})[/tex].
The total distance traveled by the particle in the given time interval is[tex]\displaystyle\frac{14}{3} \ + \ \displaystyle\frac{5}{3} \ + \ \displaystyle\frac{10}{3} \ = \ \displaystyle\frac{29}{3}[/tex].
A self-storage center has many storage rooms that are 6 feet wide, 10 feet deep, and 12 feet high. What is the volume of the room?
Answers
Answer:
720 ft^3
Step-by-step explanation:
6 * 10 *12
v = l * w * h
6 * 10 * 12 = 720
Volume is a three-dimensional scalar quantity. The volume of the self-storage centre room is 720 ft³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a room or box that is the shape of a rectangular prism is calculated by multiplying the length, width, and height of the prism.
Volume = Length × Width × Height
Given that the self-storage centre room's are 6 feet wide, 10 feet deep, and 12 feet high. Therefore, the dimension of the room can be written as,
Length = 10 ft
Width = 6 ft
Height = 12 ft
Now, the volume of the room can be written as,
Volume of the room = 10ft × 6ft × 12ft
= 720 ft³
Hence, the volume of the self-storage centre room is 720 ft³.
Learn more about Volume:
https://brainly.com/question/13338592
#SPJ5
Henry used his GPS to measure the distances from his house to two locations to the thousandth mile. Then, he rounded both values to the nearest hundredth. Which pair of distances could be the actual distances Henry measured?
school: 3.26 miles
piano lessons: 5.84 miles
Answers
Which of the following is the graph of y=x+3
Answers
Answer:ITS THE SECOND ONE
Step-by-step explanation:
Can someone help me please?
Answers
Answer:
put your equation into fractions and then see what or which 1mathces with the image
Step-by-step explanation:
a prisms base has a perimeter of 12cm and a height of 2 cm. the area of the base was 5cm. what is the surface area of the prism.
Answers
[tex]\text{Surface Area of Prism} = (2 \times \text{Base Area}) + (\text{Base perimeter} \times \text{height})\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=(2 \times 5)+(12\times 2)\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=10+24\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=34~~ \text{cm}^2[/tex]
14. What's the least common denominator of 3/4, 4/5, and 2/3?
A. 60
B. 20
C. 15
D. 12
Answers
Veronica made 960 cookies to sell. She wants to package the cookies in boxes of 16. Her goal is to make $630 from selling her cookies.
Answers
Answer: She should charge $10.50 for each box
Step-by-step explanation:
Total cookies = 960
Each box has 16 cookies
Her goal is $630
First, you want to find out how many boxes she made
960÷ 16 = 60
She made 60 boxes
Now you want to find the price for each box
630 ÷ 60 = 10.5
She should charge $10.50 for each box
I hope this helps!!!
Factorize the expressions
px2 + qx
Answers
Answer:
SOLUTION
HERE,
=X(P.2+Q)
=X(2P+Q)
Answer:
x(px+q) ( I took x as a common and the remaining are some
find the derivitive of f(x)=(x+9)/(x+1)
Answers
[tex]\dfrac{d}{dx} \left(\dfrac{x+9}{x+1}\right)\\\\\\=\dfrac{(x+1)\dfrac{d}{dx}(x+9) - (x+9) \dfrac{d}{dx}(x+1)}{(x+1)^2}\\\\\\=\dfrac{(x+1) - (x+9)}{(x+1)^2}\\\\\\=\dfrac{x+1-x-9}{(x+1)^2}\\\\\\=-\dfrac{8}{(x+1)^2}[/tex]
x-5y=16 , 4x-2y=-8 solve using elimination method
Answers
Answer:
x = -4
y = -4
Step-by-step explanation:
L1 x - 5y = 16
L2 4x - 2y = -8
4*L1 - L2
4x - 20y = 64
-4x + 2y = 8
-----------------------
-18y = 72
y = 72 / -18
y = -4
x - 5y = 16
x = 16 + 5y
x = 16 + 5(-4)
x = 16 - 20
x = -4
Help help help help math math
Answers
Answer:
<4 = 67 degrees
Step-by-step explanation:
Find <3
30+37+x=180
subtract 37 and 30
x = 180 - 30 - 37
x = 150 - 37
x= 113
Find <4
180 - 113
67
What is the solution to the equation −6z+1=−4−7z , given the replacement set {−5, −3, −1} ?
−5
−3
−1
I don't know.
Answers
the solution to the system of equation from the replacement set is -5
Given the equation −6z+1=−4−7z, we are to find the value of z from the given equation:
Given
−6z+1=−4−7z
Collect the like terms;
-6z + 7z = -4 - 1
Simplify the result
z = -4 -1
z= -5
Hence the solution to the system of the equation from the replacement set is -5
Learn more on equation here: https://brainly.com/question/2972832
Answer:
-5
Step-by-step explanation:
I took the quiz in k12
You buy candy bars at 85 cents each plus one newspaper for 60 cents. You can spend no more than $4. How many candy bars can you buy? answer
Answers
Answer:
4
Step-by-step explanation:
Well first you want to take 0.60 from the total amount which is $4 leaving you with $3.40
then you want to divide the remaining amount of money by the cost of a candy bar ($0.85)
So you do 3.40/0.85 which is equal to 4
Which of the following is a rational number?
Answers
Given 2 angles that measure 50 and 80 and a side that measure 4 feet how many triangles if any can be condctuted
Answers
Answer:
The number of unique triangles that can be constructed from the given values is; Only one triangle
Step-by-step explanation:
We are given the 2 angles of a triangle as;
∠1 = 50°
∠2 = 80°
Now, we know that sum of angles in a triangle is 180°. This means that if the third angle is denoted as ∠3, then we have;
∠1 + ∠2 + ∠3 = 180°
Thus;
∠3 = 180 - (∠1 + ∠2)
∠3 = 180 - (50 + 80)
∠3 = 180 - 130
∠3 = 50°
Thus; ∠1 = ∠3 = 50°
A triangle with two equal angles is called an isosceles triangle. Which means that it will also have 2 of its' sides to be equal.
Thus, in conclusion, only one unique triangle can be drawn.
How to do this problem
Answers
Answer: a. y=3 slope = 0
b. x=-4 slope does not exist
Step-by-step explanation:
sin(83)cos(7) + cos(83)sin(7)
Answers
Answer:
1
Step-by-step explanation:
correct on edge
sin(83 radians) * cos(7 radians)) + (cos(83 radians) * sin(7 radians)) =
0.893996664
Answer:
hope it helps
Ron wants to make money painting portraits of people at the local mall. The mall
charges Ron $22.00 a day for Ron to set up his materials to sell his portraits. He
charges $15.50 a portrait, but it costs him $3.25 in materials to make that portrait.
If x represents the number of portraits that Ron sells at the mall, which of the
following expressions would represent Ron's profit (how much money Ron will walk
away with at the end of the day)? (There is more than one answer)
12. 25x – 22.00
15.50x – 22.00
0-22.00 + 15.50x – 3.25x
15.50x
3. 25x – 22.00
22.00x – 3.25x
15.50
Answers
Answer:
A and CStep-by-step explanation:
With the amount x of portraits the daily balance is:
- $22.00+ $15.50x- $3.25xThe total is:
15.50x - 3.25x - 22.00 ⇒ 12.25x - 22.00Correct choices are A and C
With the amount x of portraits the daily balance is:
- $22.00
+ $15.50x
- $3.25x
The total is:15.50x - 3.25x - 22.00 ⇒ 12.25x - 22.00
Correct choices are A and CPlease help with this question !!
Answers
Answer:
c) i^337 is equivalent to the expression i^137
A line has a slope of and passes through the point (4, 7). What is its equation in
slope-intercept form?
Answers
Answer:
y = (7/4)x + 0
Step-by-step explanation:
yeah-ya....... right?
How do you add fractions with a whole number? Please explain the rules of it too! To be marked as brainliest
Answers
9/4 = 21/4 therefore, 9/4 = 21/4
24/10 try to reduce the numerator and denominator by a common denominator 24/10 divided 2/2 = 12/5
16/2 divided 2/2 = 8/1 = 8
I hoped that help!<3
Which of the following is equal to 2,952 ÷ 24?
A.
(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)
B.
(2,400 + 24) ÷ (480 + 24) ÷ (72 + 24)
C.
(2,400 + 24) + (480 + 24) + (72 + 24)
D.
(2,400 ÷ 24) - (480 ÷ 24) - (72 ÷ 24)
Answers
Answer:
A
Step-by-step explanation:
After doing long division we then know that 2,952 ÷24 = 123
We 1st follow pemdas knowing this we solve the equations in parenthesis 1st
(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)
2,400 ÷ 24 = 100
480 ÷ 24 = 20
72 ÷ 24 = 3
We can then rewrite the equation as
100 + 20 + 3 We then solve left to right
100 + 20 = 120
120 + 3 = 123
Helpppppppp me …………………..
Answers
Answer:
first let's solve for x
x + (x + 30) + 2x = 180
4x + 30 = 180
-30 -30
4x = 150
/4 /4
x = 37.5
Now solve for the angle measures:
(x + 30) = (37.5 + 30) = 67.5
2x = 2(37.5) = 75
x = 37.5
Answer:
X= 37.5
Step-by-step explanation:
How do I simplify the ratio of
42 : 28 : 21
Answers
Answer:
6:4:3
Step-by-step explanation:
each can be divided by 7
Answer:
6 4 3
Step-by-step explanation:
Match each shape with its area formula.
Answers
square: A=s^2
triangle: A=(1/2)bh
rectangle: A=lw
parallelogram: A=bh
A group of pigs and ducks has a total of 40 feet. There are twice as many ducks as pigs. How many of each animal are there?
Answers
The question relates to the total number of pairs of feet ducks and a pigs
are known to have.
There are 5 pigs and 10 ducksReasons:
The length of the group of ducks and pigs = 40 feet
Number of ducks = Twice the number of pigs
Each duck has 2 feet.Each pig has 4 feet.Let x represent the number of pigs, and let y represent the number of ducks, we have;
y = 2 × x
4·x + 2·y = 40
Which gives;
4·x + 2 × (2·x) = 40
8·x = 40
x = 40 ÷ 8 = 5
The number of pigs, x = 5y = 2 × x
Therefore;
y = 2 × 5 = 10
The number of ducks, y = 10Learn more about solving word problems in mathematics here:
https://brainly.com/question/25272317
A bakery sold a total of 500 cupcakes in a day, and 190 of them were vanilla flavored. What percentage of cupcakes sold that day were vanilla flavored?
Answers
Answer: 50/19
Step-by-step explanation:
I'm no math genius however I believe this is division.
500/190 gave me a fraction which is 50/19.
#13) Mrs. Frye says that the following triangles are congruent. Is she correct? Why or why not?
Answers
Answer: The following triangles are congruent.
Some one help me? ill give 50 points
Answers
Answer:
v=[tex]\frac{(w+v)/t}{2}[/tex]
Step-by-step explanation:
just inverse operations and you will always get your answer :)