. A particle moves on a line away from its initial position so that after t seconds its distance is s = 3t^2+tmeters from its initial position. (a) At what time does the particle have a velocity of 25 m/s? (b) Is the acceleration ever 0? Why or why/not? Explain your answer
pls solve and explain fast
Answers
Answer:
The velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].
Acceleration is constantly [tex]6\; {\rm m\cdot s^{-2}}[/tex] (and thus is never [tex]0[/tex].)
Step-by-step explanation:
The distance between the particle and the initial position is the displacement of this particle. Let [tex]x(t)[/tex] denote the displacement (in meters) of this particle at time [tex]t[/tex] (in seconds.) The question states that [tex]x(t) = 3\, t^{2} + t[/tex].
Differentiate displacement [tex]x(t)[/tex] with respect to time [tex]t[/tex] to find the velocity [tex]v(t)[/tex] (in [tex]{\rm m \cdot s^{-1}}[/tex]) of this particle:
[tex]\begin{aligned}v(t) &= \frac{d}{d t}\left[x(t)\right] \\ &= \frac{d}{d t}\left[3\, t^{2} + t\right] \\ &= 6\, t + 1 \end{aligned}[/tex].
Set velocity to [tex]25\; {\rm m\cdot s^{-1}}[/tex] and solve for time [tex]t[/tex] (in seconds):
[tex]v(t) = 25[/tex].
[tex]6\, t + 1 = 25[/tex].
[tex]t = 4[/tex].
Thus, the velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].
Differentiate velocity [tex]v(t)[/tex] with respect to time [tex]t[/tex] to find the acceleration (in [tex]{\rm m\cdot s^{-2}}[/tex]) of this particle:
[tex]\begin{aligned}a(t) &= \frac{d}{d t}\left[v(t)\right] \\ &= \frac{d}{d t}\left[6\, t + 1\right] \\ &= 6\end{aligned}[/tex].
In other words, the acceleration of this particle is constantly equal to [tex]6\; {\rm m\cdot s^{-2}}[/tex]. Hence, the acceleration of this particle is never [tex]0[/tex].
Related Questions
You need 3 sticks of butter for every 24 giant cookies you bake.
Answers
Answer:
Sticks of butter : 2
Number of cookies : 40
Step-by-step explanation:
Given that :You need 3 sticks of butter for every 24 giant cookies you bake.
----------------------------------------------------------------------------------------------------------
Sticks of butter Number of cookies
3 24
x 16
5 y
----------------------------------------------------------------------------------------------------------
Let the unknown be x and y..
Since you need 3 sticks of butter for every 24 giant cookies you back
Then 24/3 = 8
Since the number of cookies is 16 then 16/8 = 2
Thus x = 2
Next for y.
Since you need 3 sticks of butter for every 24 giant cookies you back
Then 5 * 8 = 40
Thus, y = 40
----------------------------------------------------------------------------------------------------------
Completed table below:
Sticks of butter Number of cookies
3 24
2 16
5 40
----------------------------------------------------------------------------------------------------------
~lenvy~
Answer:
See below ↓
Step-by-step explanation:
Given
You need 3 sticks of butter for every 24 cookiesBase rate
no. of butter sticks / no. of cookies3 / 241 stick of butter for every 8 cookies16 cookies
No. of sticks = 16/8No. of butter sticks = 25 butter sticks
No. of cookies = 8 x 5No. of cookies = 40What is the outlier for the data set? PLS HELP I REALLY NEED HELP :(
Heart Rate
5 0 7
6 3 5 6 8 8
7 0 2
8
9 0
5 0 = 50 beats per minute
40
50
68
90
Answers
Answer:
6 3 5 6 8 8
Step-by-step explanation:
number is farthest apart from others
Answer:
The correct answer is 90
Step-by-step explanation:
90 is the biggest number in the number set so therefore it is an outlier.
Have an amazing day!!
Please rate and mark brainliest!!
HELLPPPP REALLLLYYY NEEDDD
THISS ANSWER
Answers
Answer:
we need a picture to help
Step-by-step explanation:
Answer:
what is the question man stop messing around
The quotient of w and 7 is less than 17.
Answers
Answer:
17 < w / 7 is my answer. I am not sure to correct.
Kyle lives in a state that has a 6% (or 0.06) sales tax. If c represents the cost of an item and t represents the sales tax on the item, which equation expresses the relationship between these two variables?
Group of answer choices
t = 6c
t = 0.6c
t = 0.06c
t = c + 0.06
Answers
Answer:
The answer is the 3rd option
t = 0.06c
Answer:
t = 0.06c
Step-by-step explanation:
Susan has a collection of 44 nickels and dimes. If the number of nickels is three times the number of dimes, how many nickels and how many dimes does she have?
Answers
Answer:
33 nickels and 11 dimes
Step-by-step explanation:
11*3= 33
11 + 33 = 44
A trough contains a certain amount of sand. After Jamie used it to fill 2.4-kilogram bag, a 650- gram bowl, and a 3-kilogram, 125- gram pail, she realized she had a kilogram of sand left in the trough. How much sand was in the trough at first?Give your answer in grams, using a comma.
Explain how you got your answer
Answers
Answer:
7kg 275g
Step-by-step explanation:
hope this helps
Answer:
7kg 275g
Step-by-step explanation:
Add all of them together and then add what's left. Hope this helps! :)
please help! What is 75 % of 62-(98/4)
Answers
Answer:
28.13
Step-by-step explanation:
62 - (98/4)
62 - 24.5 = 37.5
75% of 37.5 is 28.125, or 28.13.
Answer:
22
Step-by-step explanation:
98/4 = 24.5
62-24.5 = 37.5
75% of 37.5
= about 22
Suppose that two cards are randomly selected from a standard 52-card deck.
(a) What is the probability that the first card is a spade and the second card is a spade if the sampling is done without replacement?
(b) What is the probability that the first card is a spade and the second card is a spade if the sampling is done with replacement?
Answers
Answer:
A) 4 of the 52 cards are queens on the first draw; 3 of the remaining 51 cards are queens on the second draw: (4/52)*(3/51)
B) 4 of the 52 cards are queens on each draw: (4/52)*(4/52)
Step-by-step explanation:
correct me if. wrong
Please help i really dont like iready and im really confused. thank you!
Answers
Answer:
15 inches cubed
Step-by-step explanation:
length 2 1/2 in
width 1 1/2 in
height 4 in
V= = l x w x h
V = 2 1/2 x 1 1/2 x 4
60/4 = 15
jill has a small treasure box
Answers
=small treasure box in possession of jill
arrange in descending order
Answers
Answer:
7 / 16, 3 / 7, 1 / 5
Step-by-step explanation:
1 / 5 = 0.2
3 / 7 = 0.428
7 / 16 = 0.4375
In descending order,
0.4375, 0.428, 0.2
Hence the answer is 7 / 16, 3 / 7, 1 / 5
7/16,3/7.1/5
Step-by-step explanation:
1/5 = 0.2
3/7= 0.428
7/16 = 0.4375
In descending order,
0.4375, 0.428. 0.2
Find the equation of the tangent to the circle x2 + y2 = 109 at point (-10,3)
Answers
Answer:
10x - 3y = -109 .
Step-by-step explanation:
x^2 + y^2 = 109
Implicit Differentiation:
2x + 2y.y' = 0
y' = -2x/2y = -x/y
So at the point (-10,3) the gradient of the tangent is -(-10)/3 = 10/3.
Equation of the tangent:
y - y1 = m(x - x1)
y - 3 = 10/3(x + 10)
y - 3 = 10/3 x + 100/3
3y - 9 = 10x + 100
-109 + 3y = 10x
10x - 3y = -109
Which fraction equals 29 }}16 ?
Answers
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answers
Answer:13.1
Step-by-step explanation:
Area equation:S=[tex]S=\frac{1}{2} ab sinθ[/tex]
The 92 children who were asked when they took their first lesson
Answers
Answer:
I need more to solve!!
Have an amazing day!!
The price of a used car that Billy is buying is $5,000. If he has to pay 8% in taxes, how much will be have to pay for the car including taxes?
Answers
Answer:
5400
Step-by-step explanation:
8% of 5000 is 400. 5000 + 400 - 5400.
Answer:
$5400
Step-by-step explanation:
We need to find the amount of tax in $
So, if 100% = $5000
8% = ?
cross multiply to be : 8 × 5000
100
to get $400
Add it to the $5000 to get $5400
Find the area of the triangle.
16 ft
20 ft
Please help
Answers
NOW I NEED HELP NOW PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Mya is redecorating her bedroom. The room is in the shape of right rectangular prism.
The dimensions of the room are: 12 feet in length by 14 feet in width by 8 feet in height.
She plans to cover the floor with tile. The cost of the tile is $4 per square foot.
She plans to cover the walls and the ceiling with paint. Each container of paint costs $16 and can cover 146 ft².
What is the total cost of the tile flooring and paint needed for this room?
Drag and drop the responses to correctly complete these sentences.
The total square feet of flooring needed is ____ and the flooring cost will be ____
The total square feet that will need to be painted is ____ and the paint cost will be ____
The total cost of the tile flooring and paint needed for this room is ____
Answers
Answer: took the test and the answers are at the bottom. cheers mate :)
Step-by-step explanation:
Reflect the given triangle over
the x-axis.
[_
3 6 31
-3 3 3.
3 [?]
13
UD
[
Answers
[3 6 3]
( 3 3. 3]
THIS ANSWER IS CORRECT
Solution:
[tex]\sf \left[\begin{array}{ccc}3&6&3\\3&-3&-3\end{array}\right][/tex]
Explanation:[tex]\sf \left[\begin{array}{ccc}3&6&3\\-3&3&3\\\end{array}\right][/tex]
The rule for a reflection over the x -axis is (x,y) → (x,−y)
===============================================================
or multiply the matrix with: [tex]\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right][/tex]
[tex]\dashrightarrow \ \sf \begin{pmatrix}1\cdot \:3+0\cdot \left(-3\right)&1\cdot \:6+0\cdot \:3&1\cdot \:3+0\cdot \:3\\ 0\cdot \:3+\left(-1\right)\left(-3\right)&0\cdot \:6+\left(-1\right)\cdot \:3&0\cdot \:3+\left(-1\right)\cdot \:3\end{pmatrix}[/tex]
Final answer:[tex]\sf \left[\begin{array}{ccc}3&6&3\\3&-3&-3\end{array}\right][/tex]
Single post math redo question
Answers
Answer:
See attached graph
Step-by-step explanation:
We need to convert the polar coordinates into Cartesian coordinates using the rules [tex]x=r\:cos\theta[/tex] and [tex]y=r\:sin\theta[/tex] (see table in attached file).
The converted points will start to resemble a circle with a horizontal pole and a diameter of 4, so by connecting the points, we get our equation [tex]r=4\:cos\theta[/tex].
The digits 5, 7, 1, and 9 are to be used in a roll number in a school. How
many different roll numbers are possible if repetitions are not permitted?
Answers
Answer:
1, 7, 5, 9
7, 1, 9, 5
9, 5, 1, 7
But there are about 10 possible combinations.
Step-by-step explanation:
Carl is arranging 86 chairs for a
dinner party. Carl places 5 chairs at
each table. Any remaining chairs will
be set aside. How many tables will
have 5 chairs?
Answers
f(x)=−2x+3; Domain: {−1,0,2}
Find the range of the function for the given domain.
Answers
Answer:
Range: 1,3,7
Step-by-step explanation:
(-1,1),(0,3),(2,7)
2(-1)+3
2(0)+3
2(2)+3
PLEASE HELP ME WILL GIVE BRAINLIEST
Answers
Answer:
1 3/4, 0
Step-by-step explanation:
You have to go 1 3/4 to the right and 0 up.
Carly is in charge of bringing juice for the class party. Her class has 24 students and 1 teacher. She estimates that each person will drink 400 milliliters of juice. To make sure she has enough, she also wants to bring an extra liter of juice. How many liters of juice should Carly bring in all?
Answers
Answer:
10,000
Step-by-step explanation:
if it's including the teacher then it should be 10,000
If it’s 1 pm what time will it be in 30 hours
Answers
Answer:
7pm
Step-by-step explanation:
1pm + 24 = 1pm
30 - 24. = 6
1pm + 6 = 7pm
The area of a rectangular field is 1.12×10^45 square feet. If the length of the field is 7×10^11 feet, and the width of the field can be written as 1.6×10x feet, what is the value of x?
Answers
Answer:
x = 10^34
Step-by-step explanation:
length × width = area
area/length = width
width = (1.12 × 10^45 ft²)/(7 × 10^11 ft)
width = 1.12/7 × (10^45)/(10^11) ft
width = 0.16 × 10^34 ft
width = 1.6 × 10^34 ft
width = 1.6 × x ft
x = 10^34
The value of x is [tex]10^3^2[/tex] or [tex]\rm x =10^3^2[/tex]
It is given that the area of a rectangular field is [tex]\rm 1.12\times10^4^5 \ feet^2[/tex]
It is required to find the value of x
What is the area of the rectangle?It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.
The formula for finding the area of a rectangle is given by:
Area of rectangle = length × width
We have:
Area of rectangle = [tex]\rm 1.12\times10^4^5 \ feet^2[/tex]
The length of the rectangle = [tex]7\times 10^1^1[/tex] feet
The width of the rectangle = [tex]\rm 1.6\times 10x[/tex] feet
After putting the values in the formula, we get:
[tex]\rm 1.12\times10^4^5 =7\times 10^1^1\times\rm 1.6\times 10x[/tex]
[tex]\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\[/tex]
[tex]\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\\\\rm x = 0.1\times 10^3^3[/tex]
[tex]\rm x =10^3^2[/tex]
Thus, the value of x is [tex]10^3^2[/tex]
Learn more about the area here:
https://brainly.com/question/14383947
Can anyone help me on this question?
Answers
hi there im giving brainliest to the most accurate answer.