find the derivative
f (x ) = (x-5)^2 (3-x)^2​

Answers

Answer 1

Given:

The function is

[tex]f(x)=(x-5)^2(3-x)^2[/tex]

To find:

The derivative of the given function.

Solution:

Chain rule of differentiation:

[tex][f(g(x))]'=f'(g(x))g'(x)[/tex]

Product rule of differentiation:

[tex][f(x)g(x)]'=f(x)g'(x)+g(x)f'(x)[/tex]

We have,

[tex]f(x)=(x-5)^2(3-x)^2[/tex]

Differentiate with respect to x.

[tex]f'(x)=(x-5)^2\dfrac{d}{dx}(3-x)^2+(3-x)^2\dfrac{d}{dx}(x-5)^2[/tex]

[tex]f'(x)=(x-5)^2[2(3-x)(0-1)]+(3-x)^2[2(x-5)(1-0)][/tex]

[tex]f'(x)=(x^2-10x+25)(-6+2x)+(9-6x+x^2)(2x-10)[/tex]

[tex]f'(x)=(x^2)(-6)+(-10x)(-6)+(25)(-6)+(x^2)(2x)-10x(2x)+25(2x)+(9)(2x)+(-6x)(2x)+x^2(2x)+9(-10)+(-6x)(-10)+x^2(-10)[/tex]

On further simplification, we get

[tex]f'(x)=-6x^2+60x-150+2x^3-20x^2+50x+18x-12x^2+2x^3-90+60x-10x^2[/tex]

[tex]f'(x)=(2x^3+2x^3)+(-6x^2-20x^2-12x^2-10x^2)+(60x+50x+18x+60x)+(-90-150)[/tex]

[tex]f'(x)=4x^3-48x^2+188x-240[/tex]

Therefore, the derivative of the given function is [tex]f'(x)=4x^3-48x^2+188x-240[/tex].


Related Questions

Find the distance between the points ( 19,-5) and ( 11, 10).

Answers

Answer:

Let the given two points be A & B. Let A ( 19 , - 5 ) be ( x₁ , y₁ ) & B ( 11 , 10 ) be ( x₂ , y₂ )

Remember : The formula to find out the distance between any two points is [tex] \tt{ \sqrt{( x_{2} -x _{1}) ^{2} + (y _{2} - y_{1}) ^{2} }} [/tex] .

[tex] \large{ \tt{✺ \: SOLUTION}} : [/tex]

[tex] \large{ \boxed{ \tt{AB = \sqrt{(x_{2} - x_{1}  ) ^{2} + (y_{2} - y_{1}) ^{2}   } }}}[/tex]

[tex] \large{ \tt{⟶ \sqrt{(11 - 19)^{2} + (10 - ( - 5) ^{2} } }}[/tex]

[tex] \large{ \tt{⟶ \sqrt{ {8}^{2} + {15}^{2} } }}[/tex]

[tex] \large{ \tt{⟶ \: \sqrt{64 + 225} }}[/tex]

[tex] \large{ \tt{⟶ \sqrt{289}}} [/tex]

[tex] \boxed{ \large{ \tt{⟶ \: 17 \: \text{units}}}}[/tex]

And we're done! Let me know if you have any questions regarding my answer :)

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁


anyone mind helping me with this problem?

Answers

Answer:

x= √65, so B is the answer

What angle is formed by the arms of a clock when the time is 6:50 a.m

Answers

the angel would be 95°
x=300°-(180°+24.99999)
300-204.99999
then round
so 95°

A local school newspaper's editor wants to survey students to determine the approval rating of the current student council president. How would the newspaper apply the cluster sampling method to find this information?
A. The newspaper staff surveys only the female students in the entire school.
B. The newspaper staff surveys random students from every grade in the school.
C. The newspaper staff surveys every student in a randomly selected grade.
D. The newspaper staff surveys 30 students from each grade in the school.

Answers

Answer:

B

Step-by-step explanation:

The correct option is B.

The newspaper staff surveys random students from every grade in the school.

Cluster sampling

In cluster sampling, researchers divide a population into smaller groups known as clusters. They then randomly select among these clusters to form a sample. Cluster sampling is a method of probability sampling that is often used to study large populations, particularly those that are widely geographically dispersed.

What is an example of cluster sampling?

An example of single-stage cluster sampling – An NGO wants to create a sample of girls across five neighboring towns to provide education. Using single-stage sampling, the NGO randomly selects towns (clusters) to form a sample and extend help to the girls deprived of education in those towns.

Learn more about cluster sampling here https://brainly.com/question/9910540

#SPJ2

I stores having a sale on jellybeans in trail mix. For 2 pounds of jellybeans and 12 pounds of trail mix, the total cost is $23. For 5 pounds of jellybeans and 3 pounds of trail mix, the total cost is $17. Find the cost for each pound of jellybeans and each pound of trail mix

Answers

Answer: The cost of each pound of jellybean is $2.5

The cost for each pound of trail mix is $1.5

Step-by-step explanation:

Let the cost for each pound of jellybeans be x.

Let the cost of each pound of trail mix be y.

Based on the information given, we can form an equation which will be:

For 2 pounds of jellybeans and 12 pounds of trail mix, the total cost is $23. This will be:

2x + 12y = 23 ...... i

For 5 pounds of jellybeans and 3 pounds of trail mix, the total cost is $17. This will be:

5x + 3y = 17...... ii

2x + 12y = 23 ...... i

5x + 3y = 17...... ii

Multiply equation i by 5

Multiply equation ii by 2

10x + 60y = 115 ...... iii

10x + 6y = 34 ..... iv

Subtract iv from iii

54y = 81

y = 81/54

y = 1.5

The cost for each pound of trail mix is $1.5

From equation i

2x + 12y = 23

2x + 12(1.5) = 23

2x + 18 = 23

2x = 23 - 18

2x = 5

x = 5/2 = 2.5

The cost of each pound of jellybean is $2.5

What is the volume of a cube
of ice with a 3 cm edge?

Answers

Answer:

27 cm

Step-by-step explanation:

every side of a cube is equal to each other. the formula for volume is LxWxH, so 3*3*3=27

Please help answer these math riddles

Answers

Answer:

Challenge B is 1.827

Step-by-step explanation:

I need more letters to submit this.

in induction, you look for a pattern and then form an educated guess or?

Answers

Answer:

look for a pattern then take an estimate or 'educated guess'

Step-by-step explanation:

Answer:

The answer is conjugation

Hope this helps!

HELP ME PLEASE!!!!!
The 2 questions is down below with the picture; please let me know.

Answers

Given:

1. 60 is the sum of 15 and Mabel's age.

2. Given equation is

[tex]-8(x+1)=-40[/tex]

To find:

1. The equation for the given situation.

2. Complete the two column proof.

Solution:

1.

60 is the sum of 15 and Mabel's age.

Let m be the Mabel's age. Then,

[tex]15+m=60[/tex]

Therefore, the required equation for the given situation is [tex]15+m=60[/tex].

2.

The complete two column proof is:

        Steps                                            Reasons

[tex]-8(x+1)=-40[/tex]                                   Given equation

[tex]\dfrac{-8(x+1)}{-8}=\dfrac{-40}{-8}[/tex]                                  Division Property of Equality

[tex]x+1=5[/tex]                                               Simplifying

[tex]x+1-1=5-1[/tex]                                   Subtraction Property of Equality

[tex]x=4[/tex]                                                     Simplifying

Wylie is renting a bicycle from a local shop that charges $5 to rent a helmet, plus an hourly rate of $8.50 for the bike. For how long can Wylie rent a bicycle if he pays a total of $47.50? Enter your answer in the box.
hours

Answers

Answer:

Wylie can rent a bike for 5 hours.

Step-by-step explanation:

Since Wylie is renting a bicycle from a local shop that charges $ 5 to rent a helmet, plus an hourly rate of $ 8.50 for the bike, to determine for how long can Wylie rent a bicycle if he pays a total of $ 47.50 the following calculation has to be done:

(47.50 - 5) / 8.50 = X

42.50 / 8.50 = X

5 = X

Therefore, Wylie can rent a bike for 5 hours.

Classify the quadrilateral.

Answers

Answer:

B Kite.

Step-by-step explanation:

It has 2 distinct pairs of equal size.

Answer:

B) kite

Step-by-step explanation:

Kite has two pairs of equal-length adjacent sides

work out 5 3/5 divided by 2 2/3 in the simplest form​

Answers

Answer:

2.1

Step-by-step explanation:

The answer is 2.1

Thank me by clicking on the heart ❤️

Is the relation exponential or linear or neither (15,10)(16,20)(17,40)(18,70)

Answers

9514 1404 393

Answer:

  neither

Step-by-step explanation:

The x-values have a common difference of 1. The y-values have first differences of 10, 20, 30. The second differences are constant at 10, indicating a quadratic relation.

The relation is neither exponential nor linear.

_____

y = 5x^2 -145x +1060

Roderick has an Internet service that charges by the hour. This piecewise function shows the cost of the Internet service based on the number of hours that Roderick uses
the Internet.
when x 34
10
(10 + 2.50(x-4)
when x > 4
Last month, Roderick used the Internet for 7.5 hours. What was he charged?
Helppppp Plssssssss

Answers

Answer:

18.75 is the answer

Step-by-step explanation:

since the internet usage is more than 4 hrs, the second equation will be used. that is

cost = (10 + 2.50 (x - 4)) where x is the usage hours.

thus

[tex]cost = 10 + (2.5 \times (7.5 - 4)) \\ = 10 + (2.5 \times 3.5) \\ = 10 + 8.75 \\ = 18.75[/tex]

Andrew walks 2000 feet from his house to his office. What distance does he cover?
A. 18,000 in.
B. 24,000 in.
C. 25,000 in.
D. 30,000 in.

Answers

The answer is B. 24,000 in.

Mike is saving up for a computer. He has $200 saved already. To earn more,
he works part-time at a job that pays $15 per hour. Let y represent the price of
the computer he chooses, and let x represent the number of hours he works.
To purchase the computer, he will need to save at least y dollars.
A. ys 200 + 15x
B. y 2 200 - 15x
C. ys 15x - 200
D. y 2 200x + 15
- PREVIOUS

Answers

Answer:

200+15x

Step-by-step explanation:

he will need to save at least 200+15x

y= amount to purchase the computer

x=hours worked for $15 per hour

$200 -money already saved

y ≤ 200+15x

4. Damiel and Kianny are going to the Pizza Palace for dinner. Damiel orders 2 slices of pizza and 1 cola and has a bill that totals $12. Kianny orders 3 slices of pizza and 2 colas and has a bill that totals $19.​

Answers

Answer:

if the question is how much does the pizza and coke cost then:

1 slice of pizza is $5 and coke is $2

Step-by-step explanation:

(2×$5)+(1×$2)=$12

(3×$5)+(2×$2)=$19

1.(06.05 MC)
Albiologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard
would be able to eat the entire population. The equation is 2* - 3 = 4x + 2.
Explain to the biologist how she can solve this on a graph using a system of equations. (10 points)

Answers

6x-2 is the correct answer

[tex]Find the missing side or angle of this equation. This is not a right triangle.[/tex]

Answers

Answer:

15.6

Step-by-step explanation:

the angle = 180-61-42=77°

x = 14.sin 77/sin 61

= 14×0.97/0.87

= 15.6

Please use the following image for the next 7 questions. Keep in mind
that because XY is tangent to circle M, XY and XM form a right angle. XY is tangent to circle M at point X.

XM = 12 and YM = 43.


Questions:

1. What is the area of circle M?

2. What is the circumference of circle M?

3. Find the length of XY.

4. Find the measure of angle M.

5. Find the area of triangle XYM.

6. Find the area of the minor sector that has been created as a part of triangle XYM.

7. Find the arc length of the minor arc from point C to the point where YM intersects with the circle.

Answers

Answer:

Step-by-step explanation:

1). Since, XM is the radius of the circle,

   Therefore, area of the circle = [tex]\pi r^{2}[/tex]

                                                   = [tex]\pi (XM)^2[/tex]

                                                   = [tex]\pi (12)^2[/tex]

                                                   = 452.39 units²

2). Circumference of a circle = 2πr

                                                = 2π(XM)

                                                = 2π(12)

                                                = 24π

                                                = 75.40 units

3). By applying Pythagoras theorem in ΔYXM,

    YM² = XY² + XM²

    (43)²= (XY)² + (12)²

     1849 - 144 = (XY)²

     XY = 41.29 units

4). tan(∠M) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

                  = [tex]\frac{XY}{XM}[/tex]

    m∠M = [tex]tan^{-1}(\frac{41.29}{12} )[/tex]

              = 73.79°

5). Area of ΔXYM = [tex]\frac{1}{2}(\text{Base)}(\text{Height})[/tex]

                             = [tex]\frac{1}{2}(41.29)(12)[/tex]

                             = 247.74 square units

6). Area of the minor sector created by ΔXYM = [tex]\frac{\theta}{360}(\pi r^2)[/tex]

                                                                             = [tex]\frac{73.79}{360}(452.39)[/tex]

                                                                             = 92.73 units²

Find y if the distance between
points P and R is 25 and point R
is located in the first quadrant.
p= (3,-18) r=(10,y)

Answers

Answer:

y = 6

Step-by-step explanation:

[tex]\sqrt{(10-3)^2 + (y+18)^2} = 25 \\ 49 + y^2 + 324 + 36y = 625 \\[/tex]

y^2 + 36y - 252 = 0

(y-6)(y+42) = 0

y = 6 (accettable)

y = -42 (not accettable)

________ analysis is the statistical process of estimating the relationship between dependent and _______ variables. A. Regression, independent B. Time series, outcome C. Time series, latent D. Regression, outcome

Answers

Answer:

A. Regression, independent

Step-by-step explanation:

Regression analysis can be regarded as a statistical methods which is been utilized in estimating the relationships that exist between a dependent variable as well as one or more independent variables. It is tools used in assessment of strength of the relationship that between variables, it could be used to model future relationship between variables.

Regression analysis posses different

variations, These are;

✓ linear

✓ nonlinear

✓multiple linear,

For linear model, this equation can be used.

Y = (a + bX + ϵ)

Where

Y =Dependent variable

a =Intercept

X= Independent variable

ϵ = Residual error

b =Slope

It should be noted that Regression

analysis is the statistical process of estimating the relationship between dependent and independent

variables.

In right triangle PQR, the length of side P Q is 70, the measure of angle P is 90 degrees, and the measure of angle R is 38 degrees. How we will represents the length of side QR?

Answers

Answer:

70/sin38°

Step-by-step explanation:

According to question,we have

PQ=70 ,  ∠P=90° & ∠R=38°

We know, sine rule

So, Sin90° / QR = Sin38° / 70

on solving, we get

QR = 70 / Sin38°

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
12x – 3y = 15

Help plsss

Answers

Answer:

y=4x-5

Step-by-step explanation:

-3y = -12x+15. y = (-12x+15)/(-3). y = (-12x/-3)+(15/-3). y = 4x-5.

Which number line represents -3 < x < 1?
H
-5 4 3 2 1 1 2 3 3 4 5

Answers

Answer:

Can I see/view the picture of option 3?

Step-by-step explanation:

HELP!! PLEASE ASAP!!!!

Answers

A is the correct answer

Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y=[tex]\frac{9}{x^2} + 2[/tex]

Answers

Hope this help!!!

Have a nice day!!!

A group of students were asked if they carry a credit card. The responses are listed in the table.


If a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. Round your answer to three decimal places.

Answers

Answer:

0.383 (3 d.p.)

Step-by-step explanation:

Probability formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student owns a credit card

Let P(B) = probability that the student is a freshman

Use the given table to calculate the probability that the student is a freshman and owns a credit card:

[tex]\implies \sf P(B \cap A)=\dfrac{23}{100}=0.23[/tex]

Use the given table to calculate the probability that the student is a freshman:

[tex]\sf \implies P(B) = \dfrac{60}{100}=0.6[/tex]

To find the probability that the student owns a credit card given that they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of A given B is:

[tex]\sf P(A|B)=\dfrac{P(B \cap A)}{P(B)}[/tex]

Substitute the found values into the formula:

[tex]\implies \sf P(A|B)=\dfrac{0.23}{0.6}=0.383333...[/tex]

Therefore, the probability that the student owns a credit card given that they are a freshman is 0.383 (3 d.p.).

P(Freshman credit card holder)

23/1000.23

P(Freshman)

60/1000.60

P(Freshman credit holder|Freshman)

0.23/0.60.383

50 POINTS PLZ HELP!!!
Your boss hands you the monthly data that shows the number of orders coming in to and out of the warehouse. The data is in the table below. Explain to your boss, in complete sentences, the solution to this system and what the solution represents.

Answers

Answer:

The number of orders in is equal to the number of orders out in month 4 (April). It appears the solution represents the time at which warehouse shipments caught up with order quantities.

Step-by-step explanation:

For this table to make any sense, we have to assume that the year started with 3 orders in January, and that one order was shipped in January. Then the number of orders was 1 or 2 each month after that, and the number of orders shipped per month was 2 each month after that. That is, the tables represent year-to-date totals of orders in and out.

Alternate Interpretation

If the numbers here are actual orders in and out in each of the listed months, it appears the warehouse is getting better at shipping orders. That is, they are increasing the shipment rate by 2 orders a month each month. They will eventually ship enough to cover the total number of orders in (total of 20 by April), but total shipments through April only amount to 16 orders.

Answer:

Writing about two pages any topic that you want, such as story, project, event, idea, .etc.please Do not copy and paste from the Interne.

cuadrado de binomio
(x-2)(-2+x)

Answers

Answer:

x^2-4x+4

Step-by-step explanation:

See image below:)

Other Questions
Younes Inc. manufactures industrial components. One of its products, which is used in the construction of industrial air conditioners, is known as P06. Data concerning this product are given below: Per Unit Selling price $ 220 Direct materials $ 38 Direct labor $ 1 Variable manufacturing overhead $ 8 Fixed manufacturing overhead $ 16 Variable selling expense $ 4 Fixed selling and administrative expense $ 16 The above per unit data are based on annual production of 4,000 units of the component. Assume that direct labor is a variable cost. What is the current contribution margin per unit for component P06 based on its selling price of $220 and its annual production of 4,000 units WILL GIVE BRAINLIEST AND 20 POINTS!Find the slope of the line in the following graph using the points on the graph. Write the exact answer. Do not round. If the slope does not exist, write DNE for your answer.(-5,2)(6,7) Anyone help me please. A circle has a circumferenceof 36. What is the radius ofthe circle? Take pi to be 3.142. State the answer to one decimalplace. 999f=4,131Solve for f. Match the hominin with the best description. Late Pleistocene hominins found only in Europe, Western Asia, and Central Asia; the Shanidar site belongs to this group. Middle Pleistocene hominin; found in Africa, Asia, Europe; shows a mixture of features from previous and later hominins. what conclusions and recommendations can you make on the issue of xenophobia to government and communities? Marking brainliest Ayuda!!! Were the British justified in burning down the Senate building and White House as military targets or was it a totally unnecessary crime? Explain! which statement from the equal pay bill letter is most clearly based on a stereotypeA. it is not the role of the government role to dictate to businesses what they should pay anyway, either as minimum wage or equal pay for men and womenB. if businesses are forced to pay women the same as male earnings, that means they will have to reduce the pay for men to employ, simple economicsC. they need to make enough to support their family and allow the mother to remain home and nourish for her kids.D. it's a situation of well-meaning intentions, but negative unintended consequences Please help .. Im really stuck According to the Law of Conservation of Mass, the totalmoles of reactants in a balanced chemical equation is...?O always equal to the total moles of the products.sometimes more or sometimes less than the total moles of the products.O always more than the total moles of the products.O always less than the total moles of the products. how social media can affect self esteem After which Cold War event did the United States and the Soviet Union enter a nuclear arms race? Clara goes minature golfing. She pays $7.50 admission and $6.25 for each round of she golfs. The total amount Clara pays including admission and the rounds of golf is $26.25. Which equation can be used to determine the number of rounds of golf she did? In City Lake, researchers caught, marked, and released 213 bass. Later, they took a sample of 104 bass and found that 13 were marked. Estimate the number of bass in the lake. A. 1704 bass B. 520 bass C. 27 bass D. 1846 bass What is the name of the supercontinent in Alfred Wegeners continental drift hypothesis? Use SOH CAH TOA to identify the Tangent Z. A group of 12 friends bought tickets for an afternoon concert. However, not all of the friends were able to sit together. Tickets for floor seats cost $15 each, and tickets for tier seats cost $70 each. The total cost of the tickets was $345. How many tickets for tier seats did they purchase Explain Pleasex = 810 9 Por qu la sociedad que surgi despus de la revolucin era ms igualitaria, pero segua siendo profundamente desigual en otros aspectos?