![[Calculus] Particle At Rest Question. Show Steps, Please!](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/o94iNcyG7uyke7cj04vFqKWdViYHcQ9d.png)
Answers
Answer:
E
Step-by-step explanation:
We are given that a particle's position along the x-axis at time t is modeled by:
[tex]x(t)=2t^3-21t^2+72t-53[/tex]
And we want to determine at which time(s) t is the particle at rest.
If the particle is at rest, this suggests that its velocity at that time is 0.
Since are we given the position function, we can differentiate it to find the velocity function.
So, by differentiating both sides with respect to t, we acquire:
[tex]\displaystyle x^\prime(t)=v(t)=\frac{d}{dt}\big[2t^3-21t^2+72t-53\big][/tex]
Differentiate. So, our velocity function is:
[tex]v(t)=6t^2-42t+72[/tex]
So, we will set the velocity to 0 and solve for t. Hence:
[tex]0=6t^2-42t+72[/tex]
We can divide both sides by 6:
[tex]0=t^2-7t+12[/tex]
Factoring yields:
[tex](t-3)(t-4)=0[/tex]
By the Zero Product Property:
[tex]t-3\text{ and } t-4=0[/tex]
Hence:
[tex]t=3\text{ and } t=4[/tex]
Therefore, at the 3rd and 4th seconds, the velocity of the particle is 0, impling that the particle is at rest.
Our answer is E.
Related Questions
1
1 point
Write the fraction as an equivalent decimal.
273
100
type your answer...
Answers
Answer:
2.75 is this correct I don't understand the question very much
You will need to set the table and make your bed today. This is not always the case
because you set the table every 3 days and you make your bed every other day. When is
the next time you will have to do both activities on the same day?
Answers
Answer:
after 6 days
Step-by-step explanation:
What is the measure of an interior angle of a regular 10-gon?
Answers
Answer:
Step-by-step explanation:
I need number 7 and 8 answered
Answers
i will mark brainlyest plss helpp
Which table has a constant of proportionality between yyy and xxx of 0.30.30, point, 3?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
xxx yyy
666 222
121212 444
303030 101010
(Choice B)
B
xxx yyy
333 1.81.81, point, 8
777 4.24.24, point, 2
999 5.45.45, point, 4
(Choice C, Checked)
C
xxx yyy
444 1.21.21, point, 2
888 2.42.42, point, 4
131313 3.93.9
Answers
Answer:
The answer is C
Step-by-step explanation:
i also use khan
Answer:
table C
Step-by-step explanation:
each one is multiplied by .30
:)
2.S.3 In a behavioral study of the fruitfly Drosophila melanogaster, a biologist measured, for individual flies, the total time spent preening during a 6-minute observation period. The following are the preening times (sec) for 20 flies:54 34 24 10 16 52 76 33 31 46 24 18 26 57 32 25 48 22 48 29 19 (a) Determine the mode (s). (b) Calculate the range. (c) Construct a dotplot of the data
Answers
Answer:
Step-by-step explanation:
The raw data given can be properly expressed by a frequency table. The frequency table formed from the data given is attached to this answer.
From the frequency table,
(a) The modes of the data are 24 and 48. Thus, the data is said to be bimodal.
(b) Range = height value - least value
= 76 - 10
= 66
Range = 66
(c) A dot plot is a pictorial graph of the plot of the given data. The plot of the given data is attached to this answer.
Please help ASAP!!!!
Answers
Answer:
E. All real values of x
Step-by-step explanation:
If you were to graph this function, it would look like a diagonal line going on seemingly forever. Therefore, the domain of h would be all values of x.
A child has $9.30 in a piggy bank. If the child spends 13 of the money on a snow cone and then finds $0.75 to put in the piggy bank, how much money does the child now have in the piggy bank?
A. $2.35
B. $3.85
C. $5.45
D. $6.95
Answers
Question 14 (5 points)
Find the equation of the line passing through the point (–1, 0) and parallel to the line y = –1∕2x + 3∕7
Question 14 options:
A)
y = ½x + ½
B)
y = –½x + ½
C)
y = 2x + 2
D)
y = –½x – ½
Answers
Slope = 1/2
Y = 1/2x + b
Plug in the point
0 = -1/2 + b, b = 1/2
Solution : y = 1/2x + 1/2
The answer is A
Write this sentence as an equation?
Six less than 4 times a number gives 18
Answers
Answer:
6-4 times x=18
btw x=9
Answer:
4x - 6 =15
Step-by-step explanation:
I will use "x" as our variable to represent the number we are trying to find.
Let's take the problem piece by piece.
Six less than four times a number.
If we are using x to represent our number, we know that when we do four times that number we are multiplying x times 4, which is the same as writing "4x."
Next we know that we are taking six less than 4x. Six less than means we will be subtracting 6 from our 4x, which is the same as writing 4x - 6.
Finally, we know that six less than 4x (4x - 6) equals 15. Now we have a full equation:
4x - 6 =15
The next Collection we will begin working on will be Collection 5, "Decisions That Matter." This Collection begins on page 251 in your textbook. Before you turn to that page, take a moment to consider the title of the Collection. What types of passages might you expect to find in this Collection? What are decisions that matter? Have you made decisions that matter? If so, what are some examples?
Turn to page 251 in your textbook. You will see an image and a quotation. How do the Collection opening image and quotation work together to make a connection? What do they have in common? What message do they send when presented together?
In this discussion board, you should complete two posts:
Original Post
Minimum of two paragraphs (4-6 sentences each) responding to the questions posed above (underlined).
Explain your thinking/reasoning.
Consider adding real life examples.
Reply to a classmate
Minimum of one paragraph (4-6 sentences) in which you elaborate on a classmates ideas, provide relatable examples or real life experience, share your opinion, or respectfully present a differing opinion.
Replies such as, "I agree," will not receive credit.
Answers
Answer:
Hope this helps ^w^
Step-by-step explanation:
Jews or Jewish people are an ethnoreligious group and Hebrews of historical Israel and Judah. Jewish ethnicity, nationhood, and religion are strongly interrelated, as Judaism is the ethnic religion of the Jewish people, while its observance varies from strict observance to complete nonobservance. This is amazing religion, how everything is in place in a neat way. the worldwide Jewish population reached a peak of 16.7 million, representing around 0.7 percent of the world population at that time, which is a ton. defines itself as a Jewish and democratic state in the Basic Laws, Human Dignity and Liberty in particular, which is based on the Declaration of Independence. Israel's Law of Return grants the right of citizenship to Jews who have expressed their desire to settle in Israel. Despite their percentage of the world's population, Jews have significantly influenced and contributed to human progress in many fields, both historically and in modern times, including philosophy, ethics, literature, politics, and cinema, medicine, and science and technology, founded Early Christianity and had a profound influence on Islam. Jews have also played a significant role in the development of Western Civilization. If you thought that was crazy watch until you hear the English word "Jew" continues Middle English '. These terms were loaned via the Old French ', which itself. In my opinion, I enjoy learning about different parts of the world. And as myself, I feel like we all should be equal no matter what race are are.
TELL ME IF YOU NEED MORE
Find the value of a/b/c if a=1/3, b=1/2, c=1/6
Answers
Answer: The answer is 0.1111111111111
Step-by-step explanation:
the table shows information about the number of tires needed for a number of cars. complete the table. write the rule of the table
I need this ASPA
Answers
Answer:SAMEEEEEEEEEEE UHHHHHHHHH
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
kjhvg
.
Step-by-step explanation:
l
Howard is picking out some movies to rent, and he has narrowed down his selections to 4 children's movies, 7 comedies, 7 mysteries, and 5 horror films. How many different combinations of 9 movies can he rent if he wants all 4 children's movies
Answers
Answer:
6188
Step-by-step explanation:
Number of children's movies = 4
Number of comedy movies = 7
Number of mystery movies = 7
Number of horror movies = 5
Total number of movies to be rented = 9 out of which 4 are fixed to be children's movies
To find:
Number of different combinations to rent 9 movies out of which 4 are children's movies
Solution:
Number of movies left to be rented = 9 - 4 = 5
Number of movies left out of which these 5 are to be rented = 7 + 7 + 5 = 17
Now, there are a total of 17 movies out of which 5 are to be selected.
Therefore, we can use:
[tex]_nC_r = \dfrac{n! }{r!(n-r)!}[/tex]
where, [tex]n = 17[/tex]
[tex]r = 5[/tex]
[tex]_{17}C_5 = \dfrac{17! }{5!(12)!}\\\Rightarrow \dfrac{17.16.15.14.13}{5.4.3.2.1} = \bold{6188}[/tex]
Write an equation of the line that
passes through the points (0,-5)
and (4,7).
Answers
Answer:
y = 3x - 5
Step-by-step explanation:
It passed through both points because of the y intercept and also the x intercept or contant matches up with the points
help pls
(screenie below)
Answers
Answer:
I thinks the answer is D nvm it's D
What is the largest integer n such that (n^2-38) / (n +1) is an integer?
a. 36
b. 38
c. 72
d. 76
e. None of these
Answers
Answer:
a. 36
Step-by-step explanation:
for (n^2-38)/(n+1) to be an integer, n+1 must completely divide, n^2-38.
we check with the options
option a n=36 sutisfies the above condition.
(36^2-38)/36+1 = 1258/37= 34 , which is an integer. Therefore, largest integer would be 36
convert 5/4 into a decimal
Answers
Answer:
Step-by-step explanation:
The answer is 1.25
The sum of 1 and a number x
Answers
9515 1404 393
Answer:
1 + x
Step-by-step explanation:
A sum is found by adding terms. Here, you are told the terms to add are 1 and x. We use the plus sign (+) to signify addition. Your sum is ...
1 + x
Choose all the expressions that are equivalent to 3(2 + 11)
32 + 311
3(2) + 3(11)
3(2) + 11
6 + 11
6 + 33
3 + 22
Answers
solve the question below 33
Answers
Answer:
The value of x(perpendicular) is 17.80
Step-by-step explanation:
Given triangle is a right angled triangle as one of the angles is 90°
Also according to the reference angle 54°,
Hypotenuse = H = 22
Perpendicular = P = x
We can use the trigonometric ratio of sine as it involves both known value perpendicular and hypotenuse.
So,
[tex]sin\ 54 = \frac{P}{H}\\sin\ 54 = \frac{x}{22}\\0.8090 = \frac{x}{22}\\x = 0.8090*22\\x = 17.798[/tex]
Rounding off to nearest hundredth
x = 17.80
Hence,
The value of x(perpendicular) is 17.80
A store receives customer satisfaction ratings that range between 0 and 100. In the first 13 ratings the store received, the average customer satisfaction rating was 75. What is the least value the store can receive for the 14th rating and still be able to have an average of at least 84 for the first 21 ratings?
Answers
Answer:
Step-by-step explanation:
From the given information:
For the first 10 ratings, the average value is 75.
For maintaining the average of 84 ratings for the first 21st rating, we have:
Total rating for 21 units = 84 * 21 = 1764
For 10 units = 84 *10 = 840
Now, the initial 10 unit average = 75 * 10 =750
The first 10 unit + last 10 unit = 840 + 750 = 1590
The difference = 1764 - 1590 =174 unit
So, in the 14th rating, he has to go with 174 units.
Which equation represents a line parallel to the line shown on the graph?
Answers
Step-by-step explanation:
b
Solve the inequality. Graph the solution.
p-4<2
help plz
Answers
Answer:
the inequality would be p<6
the graph is below.
Step-by-step explanation:
Here's how to solve the equation:
p-4<2
add 4 to both sides
p<6
The English translation of the inequality would be "p is less than 6".
please see below for the graph.
Hope this helps! :)
__ + 15 - 15 = 21
what is the blank number
Answers
Answer:
Step-by-step explanation:
21 is the blank number as +15 and -15 cancels out
Answer:
the answer is 21
Step-by-step explanation:
i need help pls help me
Answers
Answer:
8
Step-by-step explanation:
please answer correctly no trolls!
Answers
Answer:
Yes
Step-by-step explanation:
16.5-15.<3.8
Ravi buys pounds of flour. How many ounces of flour does he buy?
Answers
There is 16 ounces in each pound, how ever many pounds it is multiply 16 by the number of pounds,
Step-by-step explanation:
how ever many pounds it is multiply 16 by the number of pounds,
Ashley ran from home to school in 10 minutes. what has her average speed, if the distance between her house and her school is 1.5 miles?
Answers
Answer:
0.15 miles per minute
Step-by-step explanation:
Average speed is in distance over time, so you could write:
1.5 miles / 10 minutes
Now, simplify:
.15 miles per minute
(hope this helps :-D)
Answer:
.15 miles per minute
Step-by-step explanation:
what is the mean, mode, median, and range of the numbers 24, 31, 12, 38, 12, and 15
Answers
Answer:
mean: 19.66667
mode: 12
median: 18
range: 37