Given:
Consider the completer question is "Find the derivative [tex]\dfrac{dy}{dx}[/tex] for [tex]y=\dfrac{x^2-4x}{x^3-5}[/tex]."
To find:
The derivative [tex]\dfrac{dy}{dx}[/tex].
Solution:
Chain rule: [tex]\dfrac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)[/tex]
Quotient rule: [tex]\dfrac{d}{dx}\dfrac{f(x)}{g(x)}=\dfrac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}[/tex]
We have,
[tex]y=\dfrac{x^2-4x}{x^3-5}[/tex]
Differentiate with respect to x.
[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}\left(\dfrac{x^2-4x}{x^3-5}\right)[/tex]
Using chain rule and quotient rule, we get
[tex]\dfrac{dy}{dx}=\dfrac{(x^3-5)\dfrac{d}{dx}(x^2-4x)-(x^2-4x)\dfrac{d}{dx}(x^3-5)}{(x^3-5)^2}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{(x^3-5)(2x-4)-(x^2-4x)(3x^2)}{(x^3-5)^2}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{2x^4-4x^3-10x+20-3x^4+12x^3}{(x^3-5)^2}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}[/tex]
Therefore, the required answer is [tex]\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}[/tex].
Write an equation in slope-intercept form which has a slope of 1/4 and crosses the Ÿ-axis at (0,7)
Answer:
y= 1/4 x +7
Step-by-step explanation:
The slope intercept form of a line is
y = mx + b where m is the slope and b is the y intercept
the slope is 1/4 and the y intercept is 7
y= 1/4 x +7
I need help one this question.
Answer:
-2
Step-by-step explanation:
the y-intercept is -2
Answer:
y=2x-2
Step-by-step explanation:
Find the slope.
y1-y2/x1-x2
2-(-2)/2-0
That gives you 4/2 or a slope of 2.
The y intercept is at -2.
Y=2x-2
in desperate need of help , please help lol
Answer:
No, the figures are not similar.
Step-by-step explanation:
In order for the figures to be similar, in object B, the line labeled as 20 would need to be 10.
ANSWER ASAP !!!!!!!!!!
what is the birthday polynomial project for 05/11/2004?
Answer:
OBJECTIVE: To create, characterize and graph a polynomial function that reflects you!
PROCESS:
1. Write, IN ORDER, the digits of the month (1 or 2 digits), day (1 or 2 digits), and year (4 digits) of your birthday.
For example, April 2, 1976 could be “421976” or “4021976”. Use must use 6, 7 or 8 digits.
2. Create a polynomial using your digits, in order. Again, for example, my polynomial could be:
() = 4
5 + 2
4 − 1
3 − 9
2 + 7 −6 or
() = 4
6 + 2
4 − 1
3 − 9
2 + 7 − 6
*notice in the second example, the 0 eliminated the 5th degree term
**if your birth year is 2000, you may change your constant term (the “lagger”, which is the 6 in my
equation) to your favorite number, instead of 0.
3. Experiment with the shape of your birthday polynomial by changing the signs (+/-) of various terms in your
calculator. Try to create a polynomial function with an interesting shape and some turning points. Be creative!
You’re trying to express yourself in this graph!
*notice the change in the 2 graphs
below by just changing 3 positive
signs to negative!
4. Analyze your polynomial (using your calculator)
by finding these characteristics:
a. Roots (x-intercepts)
b. Y-intercept
c. Relative minimums and maximums
d. End behavior
e. Points (x, y)
PRODUCT: Make a presentation of your polynomial. Be creative! Be colorful! Be neat! Be artistic and ACURATE! Just
meeting the basic requirements will earn you a 90% (at most). At a minimum, your presentation should include a visual
representation of the graph of your polynomial and should also include the following:
□ The statements: My Birthday is ________________
My Birthday Polynomial is ______________________.
□ A T-chart with 10 (x, y) points
□ All Roots (labeled on graph and values)
□ Y-intercept (labeled on graph and value)
□ Relative Maximum and Minimums (labeled on graph and values)
□ Sentence description of end behavior and why this occurs
ASSESSMENT: Your project will replace lowest MID-CHAPTER QUIZ (30 points). You will be graded on completion of all
requirements and accuracy of graph and values. Additional points (90% and above) will be awarded for creativity and
effort.
YOUR PROJECT IS DUE WEDNESDAY, DECEMBER 2. ABSOLUTELY NO LATE PROJECTS WILL BE ACCEPTED. PLEASE FEEL
FREE TO EMAIL ME OVER THE BREAK IF YOU HAVE QUESTIONS… HAVE A GREAT THANKSGIVING HOLID
Step-by-step explanation:
The birthday polynomial for the date 05/11/2004 is 20040511.
The birthday polynomial is a mathematical concept that assigns a unique polynomial to a specific date, typically represented in the format MM/DD/YYYY.
To construct the birthday polynomial for a given date, follow these steps:
1. Write the date in the format MM/DD/YYYY.
2. Rearrange the numbers in reverse order, i.e., YYYY/MM/DD.
3. Remove any slashes or separators between the numbers.
To construct the birthday polynomial for the date 05/11/2004, follow these steps:
1. Write the date in the format MM/DD/YYYY: 05/11/2004
2. Rearrange the numbers in reverse order: 2004/05/11
3. Remove the slashes: 20040511
Therefore, the birthday polynomial is 20040511.
Learn more about Birthday Polynomial here:
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Can someone please help me please this is turned in like in a couple of minutes !!!!!!!!!!!!!!!
Answer:
1) 3 teaspoons
2) 16 tablespoons
3) 4 tablespoons
4) 16 oz
5) 4/6 or 2/3
6)2 cups
7) 4 cups
8) 4 quarts; 16 cups
9) 8 fl oz
10) 1
Step-by-step explanation:
Mr Mason asks 240 year 11 students what they want to do next year. 15% of the students want to go to college. ¾ of the students want to stay at school. The rest of the students do not know. Work out the number of students who do not know.
Answer:
Number of students who do not know = 24
Step-by-step explanation:
Year II students = 240
15% of the students want to go to college.
Number of year II students who wants to go to college = 15% of 240
= 15/100 × 240
= 0.15 × 240
= 36
¾ of the students want to stay at school.
Number of students who wants to stay at the school = 3/4 × 240
= (3 × 240) / 4
= 720 / 4
= 180
Number of students who do not know = Total year II students - Number of year II students who wants to go to college - Number of students who wants to stay at the school
= 240 - 36 - 180
= 24
Number of students who do not know = 24
Solve for a.
4(a + 3)=12 + 4a
−1
no solution
all real numbers
−3
Final Answer: All Real Numbers
Steps/Reasons/Explanation:
Question: Solve for a. [tex]4(a + 3)=12 + 4a[/tex].
Step 1: Expand.
[tex]4a + 12 = 12 + 4a[/tex]
Step 2: Cancel [tex]4a[/tex] on both sides.
[tex]12 = 12[/tex]
Step 3: Since both sides equal, we would have infinitely many solutions.
~I hope I helped you :)~
Answer:1
Step-by-step explanation:1
A saleswoman is paid $80 a day plus $6 for each sale she makes. She wants to earn more than $150 today. Write an inequality that represents the number of sales, x, the saleswoman must make today to earn more than $150. What is the least number of sales she must make to reach her sales goal
Answer:
12
Step-by-step explanation:
Given that:
Daily wages paid to a saleswoman = $80
Wages paid for each sale made by her = $6
Target of today's earnings = more than $150
To find:
Least number of sales to be made so that the total earnings today is more than $150.
Solution:
Number of sales for today = [tex]x[/tex]
Wages for one sale = $6
Wages for [tex]x[/tex] number of sales = $6[tex]x[/tex]
Total earnings = Per day sales + Wages for [tex]x[/tex] number of sales > $150
[tex]80 + 6x > 150[/tex]
we need to solve for above inequality to find the least number of sales to be made to meet the goal.
Subtracting 80 from both sides:
[tex]\Rightarrow 6x>70\\[/tex]
Dividing both sides by 6:
[tex]\Rightarrow x > 11[/tex]
Therefore, at least 12 sales must be made.
PLEASE HELP!!! FOR 60 POINTS!! New York City has two airports (JFK and LGA). If you’re flying with United Airlines (UA) and your primary concern is to arrive on time, is it better to fly to JFK or to LGA?
Answer:
If you're heading into New York City, LaGuardia is the closest. It's just 8.6 miles from LaGuardia to Midtown Manhattan, compared to 14.7 miles from JFK and 16.6 miles from Newark.
Step-by-step explanation:
To assess if flying with United Airlines to LGA is better in terms of arriving on time, we would have to examine the on-time performance data for United Airlines flights at both airports.
What are United Airlines flights?United Airlines is a significant American airline that flies domestically as well as internationally. The airline provides a wide range of services, such as passenger transportation, cargo delivery, and vacation packages.
The US Department of Transportation tracks and distributes on-time performance information for airlines and airports on its website. We can assess whether airport has a higher on-time performance record for this carrier by examining statistics for United Airlines trips to LGA.
LGA are both important airports that serve the greater New York City area, and both can face delays and congestion. Arrive at the airport well in advance of the scheduled departure time and check with your airline for any changes.
Therefore, to assess if flying with United Airlines to LGA is better in terms of arriving on time, we would have to examine the on-time performance data for United Airlines flights at both airports.
Learn more about United Airlines flights, here:
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At the last pep rally 3 out of every 7 students wore school colors. Based on this information, if 350 students attend the next pep rally, how many of these students will wear school colors
(1st answer will get marked brainliest.. please don’t answer if you don’t know what the answer is.. thank you :))
Answer:
150
Step-by-step explanation:
Please let me know if you still need help!
Answer:
150 students would be wearing school colors
Step-by-step explanation:
Pretty sure because you divide 350 by 7 (which gives 50), then multiply 50 by 3 to get 150, which would be 3/7 of the student population
Tom swam to the bottom of a swimming pool that was 9 feet deep and he touched
the bottom. He swam back to the surface. How many feet did Tom swim?
Answer:
18 feet
Step-by-step explanation:
9 x 2 = 18
holly has $10.00. she saw a purse in a catalog that was marked $14.95 plus 5 sales tax
Answer:Molly won't be able to pay for the purse because $14.95 plus 5 is $19.95 and Molly only has $10.00 so she won't be able to buy the purse.
Step-by-step explanation:
Answer: A. $5.70
Step-by-step explanation:
WILL GIVE BRANLIEST: What are three ordered pairs that create a relation with a domain of {−2, 1, 4}?
Answer:
(-2,1 ) (1,4) (-2,4)
Step-by-step explanation:
A number is equal to 3 times a smaller number. Also, the sun of the smaller number and 4 is the larger number. The
situation is graphed on the coordinate plane below, where x represents the smaller number and y represents the larger
nunber
Answer:
y=3x and y=x+4
that is the third option
Step-by-step explanation:
let the larger number be y and the smaller one be x
From the mathematical statements,
y=3x
Also
y=x+4
Samuel scored a 32.5/40 on his most recent math test what percent did he earn in the test round to the nearest whole percent
Answer: 81%
Step-by-step explanation:
From the question, we are informed that Samuel scored a 32.5/40 on his most recent math test.
Based on the values given, to convert it to percentage, we have to multiply the score by 100. This will be:
= 32.5/40 × 100
= 3250/40
= 81.25%
= 81% to nearest whole number
Data berikut ialah suhu yang dicatat untuk 5 hari.
The following data are the temperatures recorded for 5 days.
25°C, 27°C, 34°C, 28°C, 29°C
Hitungkan min. / Calculate the min
Jawapan / Answer:
[tex] \frac{25 + 2 7 + 34 + 28 + 29}{5} [/tex]
[tex]119.8[/tex]
In the past year, Lizet has spent $7,440 on her rent. What is her unit cost
(dollars per month)?
Answer:
$620/month
Step-by-step explanation:
$7,440 / 12 = $620
Answer:
620 a month
Step-by-step explanation:
7440÷12monthes=620 per month
can someone explain how you would get the answer to
Answer:
987654
Step-by-step explanation:
I NEEP HELP ASAP PLEASE AND THANK YOU
Answer:
The first answer, 3 times the square root of x squared is correct.
hw, can i get some help with this one? if you can, i’d appreciate an explanation on how you got the answer please :)
An office printer prints 24 photos in 8 minutes. A home printer prints 36 photos in 18 minutes. Find the unit rate of each printer. Tell which printer is the one that prints at a faster rate. please help
Answer:
office printer
Step-by-step explanation:
24/8= 3 per min
36/18= 2 per min
office printer is faster
Answer:
The office printer.
Step-by-step explanation:
If the office printer prints 24 photos in 8 minutes, then it prints 3 per minute, since 24/8=3.
If the home printer prints 36 photos in 18 minutes, then it prints 2 per minute, since 36/18=2.
13. A quadratic function passes through the points (0,5), (2,3), and (3,5). Which
function represents the same relationship?
A h(I) = x2 + 3x + 5
B h(x) = x2 – 3x + 5
C h(c) = -3x2++5
D h(c) = x2
= 2 + 5x - 3
Answer:
B
Step-by-step explanation:
( Which of the following best describes an ecosystem in a neighborhood garden?
What is the domain of f?
Chose 1 answer:
PLZ HELP I REALLY NEED HELP
state whether the relationship between x and y in y + 4x-5 is proportional or non-proportional. then graph the function
Answer:
Yes, any equation of the form y=mx +c is a proportional relationship.
Step-by-step explanation:
4(x + 2) = 2 (x – 6)
What value of x makes the equation true?
A. 1
B. -7
C.-10
D.8
Find the measure of the numbered angle.
m∠1 =
Answer:
∠1 = 50°Step-by-step explanation:
right triangle.
∠1 = 180 - 90 - 40
∠1 = 50°
On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions. The test is worth a total of 100 points. There are twice as many
2-point questions as 5-point questions on the test. How many 2-point questions are on the test?
•8
•4
•12
•16
Answer:
B. 8
Step-by-step explanation:
Calculate how many 2 point answers and 5 point answers there are.
2 x 8 = 16
Since there are half as many 5 point answers as there are 2 point answers,
5 x 4 = 20
calculate how many remaining questions there are. The numbers would be 8 since you had 8 2 point questions and 4 since half of 8 is four.
8 + 4 = 12
Subtract that number by the total questions, which is 28.
28 - 12 = 16
Next figure out how many 4 point questions you had (28-12=16)
16 x 4 = 64
To check your work add up the totals and see if they match up to 100.
16 + 20 + 64 = 100
Step-by-step explanation:
5. Solve for x.
6. Solve for
(9x - 16)
I
(3.1 + 11)
(7x - 5)
ments
X =
7 Find m
Answer:
12*56-56+11=12
Step-by-step explanation:
12 for 56