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].
cuadrado de binomio
(x-2)(-2+x)
Answer:
x^2-4x+4
Step-by-step explanation:
See image below:)
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?
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°
Find the distance between the points ( 19,-5) and ( 11, 10).
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 :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
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.
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)
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)
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
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
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.
Answer:
B
Step-by-step explanation:
The correct option is B.
The newspaper staff surveys random students from every grade in the school.
Cluster samplingIn 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
HELP!! PLEASE ASAP!!!!
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.
Which number line represents -3 < x < 1?
H
-5 4 3 2 1 1 2 3 3 4 5
Answer:
Can I see/view the picture of option 3?
Step-by-step explanation:
in induction, you look for a pattern and then form an educated guess or?
Answer:
look for a pattern then take an estimate or 'educated guess'
Step-by-step explanation:
Answer:
The answer is conjugation
Hope this helps!
What is the volume of a cube
of ice with a 3 cm edge?
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
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.
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
HELP ME PLEASE!!!!!
The 2 questions is down below with the picture; please let me know.
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
anyone mind helping me with this problem?
Answer:
x= √65, so B is the answer
________ 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
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.
Classify the quadrilateral.
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
Answer:
2.1
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
12x – 3y = 15
Help plsss
Answer:
y=4x-5
Step-by-step explanation:
-3y = -12x+15. y = (-12x+15)/(-3). y = (-12x/-3)+(15/-3). y = 4x-5.
Is the relation exponential or linear or neither (15,10)(16,20)(17,40)(18,70)
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
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]
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)
What angle is formed by the arms of a clock when the time is 6:50 a.m
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
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
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.
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.
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.
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)
23/1000.23P(Freshman)
60/1000.60P(Freshman credit holder|Freshman)
0.23/0.60.383Please help answer these math riddles
Answer:
Challenge B is 1.827
Step-by-step explanation:
I need more letters to submit this.
[tex]Find the missing side or angle of this equation. This is not a right triangle.[/tex]
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
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]
Hope this help!!!
Have a nice day!!!
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
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.