![[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/fNUowFQYtFS5tDO6erBsFFv3d9ZQRuYU.jpeg)
Answers
Find the critical points of [tex]f_1[/tex] and [tex]f_2[/tex].
By the fundamental theorem of calculus,
[tex]{f_1}'(x) = \displaystyle \prod_{j=1}^{21} (x-j)^j = (x-1) (x-2)^2 (x-3)^3 \cdots (x-21)^{21}[/tex]
and [tex]{f_1}'=0[/tex] for [tex]x\in\{1,2,3,\ldots,21\}[/tex]. The stationary points at odd values have odd multiplicity, while the even ones have even multiplicity. At the points of odd multiplicity, [tex]{f_1}'[/tex] passes through the [tex]x[/tex]-axis and the sign of [tex]{f_1}'[/tex] changes, while at the points of even multiplicity, [tex]{f_1}'[/tex] is tangent the to [tex]x[/tex]-axis. We also have
[tex]\displaystyle \lim_{x\to-\infty} {f_1}'(x) = (-1)^{1+3+5+\cdots+21} \infty = (-1)^{11^2} \infty = -\infty[/tex]
[tex]\displaystyle \lim_{x\to\infty} {f_1}'(x) = \infty[/tex]
so the plot of [tex]{f_1}'[/tex] looks more or less like the attached curve. (Not drawn to scale)
Wherever the sign of [tex]{f_1}'[/tex] changes from negative to positive, as it does in the case of [tex]x\in\{1,5,9,13,17,21\}[/tex], there is a local minimum, so [tex]m_1 = 6[/tex]. Similarly, wherever the sign changes from negative to positive, as it does when [tex]x\in\{3,7,11,15,19\}[/tex], there is a local maximum, so [tex]n_1 = 5[/tex].
Repeat for [tex]f_2[/tex].
[tex]{f_2}'(x) = 4900 (x-1)^{49} - 29400 (x-1)^{48} = 4900 (x-1)^{48} (x-7)[/tex]
has roots at [tex]x=1[/tex] and [tex]x=7[/tex], but only the latter is a critical point due to odd multiplicity. A rough sketch of the plot of [tex]{f_2}'[/tex] is also attached. The sign of [tex]{f_2}'[/tex] changes from negative to positive at [tex]x=7[/tex], so [tex]m_2 = 1[/tex] and [tex]n_2=0[/tex].
We conclude that
Q.9) [tex]2m_1+3n_1+m_1n_1 = \boxed{57}[/tex]
Q.10) [tex]6m_2+4n_2+8m_2n_2 = \boxed{6}[/tex]
![[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/bIPychf0djTPy98heIo6nG634gVENW2b.png)
![[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/hMtrhRp1JErbgUrPiBiP0nmNPl3Gi3X8.png)
Related Questions
x^3-9x^2-4x+36=0
Determine the values of x for which the function f(x)= x^2-5x-2/ 5x-3
A. is zero
B. is positive, and
C. is negative
Answers
Answer:
B
Step-by-step explanation:
use the formula x = [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]x= \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
according to the known condition, a = 1, b = -5-2/5 c = -3
you can input these values into the above two.
Identify the slope of the line. Interpret the slope in the context of this problem. Y=-2.3332x+123.98
Answers
Answer:
Slope = 2.3332
Interpretation: As increases by 1 unit, y increases by 2.332 units
Step-by-step explanation:
Equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept
Comparing y=-2.3332x+123.98 to the standard equation form we get
m = 2.3332
b = 123.98
Slope is rise/run
It tells you the change in y-value for a unit change in x-value
Here 2.332 can be interpreted to mean that as x changes by +1 value, y changes by + 2.332
The following data are an example of what type of regression?
x
1
2
3
4
5
6
O A. Exponential
OB. Quadratic
O C. Linear
OD. None of the above
y
10,960
10,808
10,904
11,286
11,876
12,553
Answers
Answer:
linear
Step-by-step explanation:
because they're are all in a vertical vay
find the perimeter and area of the figure? G( -4,1), H(4,1),I(0,-2)
Answers
Perimeter = 18 units; Area = 9 sq. units
GH = √(-4-4)²+(1-1)² = 8 units
HI = √(4-0)²+(1+2)² = 5 units
IG = √(0+4)²+(-2-1)² = 5 units
Perimeter of the given triangle = 8+5+5=18 units
Semi-perimeter of triangle = 18÷2=9 units
Using Heron's formula; √[s(s-a)(s-b)(s-c)]=Area of triangle;
A= √(9)(9-8)(9-5)(9-5)
= √(9)(3)(3)
= 9 sq. units
To learn more about this; visit: https://brainly.com/question/24701453
#SPJ9
If the tangent line to y = f(x) at (6, 4) passes through the point (0, 3), find f(6) and f'(6).
f(6) =
f'(6) =
Answers
Answers:
f(6) = 4
f ' (6) = 1/6
===========================================================
Explanation:
f(6) = 4 since the point (6,4) is on the f(x) curve. This is where the tangent is touching.
The tangent line also goes through (0,3)
Let's find the slope of the line through those two points.
[tex](x_1,y_1) = (6,4) \text{ and } (x_2,y_2) = (0,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 4}{0 - 6}\\\\m = \frac{-1}{-6}\\\\m = \frac{1}{6}\\\\[/tex]
The slope of the tangent line is 1/6. This is the value of f ' (6) because the derivative measures the tangent at the given x value. It's useful to determine the instantaneous rate of change.
what is the unit digits of 3^40
Answers
Answer:
1
Step-by-step explanation:
the answer is 1.21576655000000000.
the unit of this no. is 1.
-12[tex]-12\ \textless \ \frac{1}{2}\left(4x+16\right)\ \textless \ 18[/tex]
Answers
The solution to the given inequality is -10 < x < 5.
How to solve a compound inequality involving the and operation?
To solve a compound inequality involving the and operation, we solve each inequality, then find the intersection of these solutions.
For this problem, the inequality is given by:
-12 < 0.5(4x + 16) < 18.
Multiplying all the terms by 2:
-24 < 4x + 16 < 36
Hence:
4x + 16 > -24
4x > -40
x > -10.
4x + 16 < 36
4x < 20
x < 5
The intersection of these two solutions is:
-10 < x < 5.
More can be learned about inequalities at https://brainly.com/question/25235995
#SPJ1
help pleaseeeeeeeeee its difficult I will slide brainiest
Answers
Answer: hope this help
step-step explanation:
A rectangular block has a mass of 1088g. The dimensions of the block are 8cm by 5cm by 4cm. What is the density of the block?
Answers
Answer:
277g / 40cm³
Step-by-step explanation:
Density = mass / volume
In this case:
volume = 8cm*5cm*4cm = 160cm³
then:
Density = 1088g / 160cm³ = 544g/80cm³ = 277g/40cm³
Find the area of the figure. (Sides meet at right angles.)
5 yd
4 yd
2 yd
2 yd
yd
2 yd
4 yd
Answers
Answer:
1,024yd
Step-by-step explanation:
a=a to the second,= 32(2)= 1,024
A quadratic function is decreasing on (-∞, 3) and increasing on (3, ∞).
Will the vertex be the highest or lowest point on the graph of the parabola?
Explain.
Answers
Greetings from Brasil...
If X grows and Y grows, the function is increasing
If X increases and Y decreases, the function is decreasing
Besides that, according to the statement, we can conclude that the parabola has an upward concavity, that is, a > 0. In this case the vertex will be a minimum point
check the attachments
P.S. - vertex coordinate = (3; 0)
If we are asked to to find the x-intercept of the graph given its equation, we substitute y = 0 into the equation, because:
The x-intercept is the point where the graph intersects the x-axis and hence the y-coordinate of that point will be 0
The y-intercept will be 0
The x-intercept is the point where the graph intersects the y-axis and hence the y-coordinate of that point will be 0
The x-intercept is always at (0, 0)
Answers
Answer:
the answer will be c....
The correct option is The x-intercept is the point where the graph intersects the x-axis and hence the y-coordinate of that point will be 0.
What are intercepts?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Given that, we are asked to find the x-intercept of the graph given its equation, we substitute y = 0 into the equation,
So, if we are asked to find the x-intercept, so simply by the definition of intercepts we are asked to find where is the line cutting the x-axis, and as we know that, when a line cuts x-axis its y-intercept we automatically be 0.
So, the answer to this will be, the line cut the x-axis is its x-intercept thus, making y-intercept zero.
Hence, the correct option is the x-intercept is the point where the graph intersects the x-axis and hence the y-coordinate of that point will be 0
Learn more about intercepts, click;
https://brainly.com/question/14180189
#SPJ2
Graph the numbers -0.2, 7/10, -1, √2, and -4 on a number line.
-8 -7, -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Answers
Answer:
Step-by-step explanation:
What is the answer to this help (number 4.)
Answers
19. 9a2b = c + 4a, for a
Answers
Answer:x/5 + 2b/5
Step-by-step explanation:
9a-2b=c+4a solve for a
9a-2b=c+4a
add -4a to both sides
9a-4a-2b=x+4a-4a
5a-2b=x
add 2b to both sides
5a-2b+2b=x+2b
5a= x+2b
divide by 5
5a/5 = x/5 +2b/5
a= x/5 + 2b/5
Name the intersection of line AB and line CB
Answers
Answer:
B
Step-by-step explanation:
I am not sure what kind of help you need here. the answer is kind of obvious, already revealed by the names of the lines (AB and CB). they meet or intersect at their joined point B.
17.
Peter transports metal bars in his van.
The van has a safety notice: "Maximum Load 1200 kg".
Each metal bar has a label: "Weight 60 kg".
For safety reasons, Peter assumes that:
1200 is rounded correct to 2 significant figures, and
60 is rounded correct to 1 significant figure.
Calculate the greatest number of bars that Peter can safely put into the van if his assumptions are
correct.
Answers
Answer:
17 bars
Step-by-step explanation:
Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.
Range of valuesThe error in a rounded number is assumed to be as much as half of the least significant digit of the number.
Peter's load limit may actually be as low as ...
1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100
Peter's bar weight might be as high as ...
60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10
Safe loadingIf Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...
(1150 kg) / (65 kg/bar) ≈ 17.7 bars
The greatest number of bars Peter can load safely is 17.
DES
Question: 2/20
Find the next number in the sequence: 1, 1, 2, -1, 1, -2, -1,
Answers
Eigenvalues are the special set of scalar values that is associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed as characteristic roots. It is a non-zero vector that can be changed at most by its scalar factor after the application of linear transformations.
0 Eigenvalue
3 Eigenvalue
The y values of any nxn matrix A that adhere to the following criteria are considered to be its eigenvalues.
When I is the order n identity matrix, det(A - yI) = 0.
In this case, A = [1 2; 1 2], I = [1 0; 0 1], and yI = [y 0; 0 y]. I've added a new line in this notation with ;.
A - yI = [1-y 2; 1 2-y]
det(A - yI) = 1 - y* In other words, - 2 = = 2 - y - 2y + y2 - 2 = 0 = y2 - 3y = 0 = y(y-3) = 0.
y = 0 or y - 3 = 0
y = 3
To learn more about Eigenvalues Visit : https://brainly.com/question/13144436
#SPJ9
27. If Q is the midpoint of PR, find the coordinates of R if
P (3,-5) and Q (-1,2)?
Answers
Answer: -5,9
Step-by-step explanation:
The following information is available for Trinkle Company for the month of June:
The unadjusted balance per the bank statement on June 30 was $53,382.
Deposits in transit on June 30 were $2,545.
A debit memo was included with the bank statement for a service charge of $11.
A $3,339 check written in June had not been paid by the bank.
The bank statement included a $1,350 credit memo for the collection of a note. The principal of the note was $1,325, and the interest collected amounted to $25.
Required
Determine the true cash balance as of June 30. (Hint: It is not necessary to use all of the preceding items to determine the true balance.)
Answers
True Cash Balance As on June 30 is mathematically given as $ 52588
This is further explained below.
What is the true cash balance?As of the Bank Statement dated June 30th, the Unadjusted Balance A = $53,382.
Deposit in Transit June B = $2,545.
Outstanding Check June 30 C = $3,339
Generally, the equation for the true cash balance is mathematically given as
cash balance = A-(C-B)
Therefore
cash balance= 53,382-(3,339-2,545.)
cash balance= 52588
In conclusion, True Cash Balance As on June 30 = $ 52588
Read more about true cash balance
https://brainly.com/question/15359741
#SPJ1
How do I find out the check amount before the tip when the total amount was $55 with a 10% tip
Answers
Answer:$49.50
Step-by-step explanation:
First you have to find what 10% of 55 is. So if you times 10% by 55 you come out with $5.5. So after that you must subtract 5.5 from 55 which comes out to $49.50.
Evaluate the following expression if a = -3 and b = 4. Square root 361 - 2a2 - [b - 17]
Answers
Given that a = -3 and b = 4, the numerical value of the expression (√361 - 2a² - [b - 17]) is 14.
What is the numerical value of the expression?Given that;
√361 - 2a² - [b - 17]a = -3b = 4To determine the numerical value of the expression, replace all the occurrence of a and b with -3 and 4 in the respectively and simplify.
√361 - 2a² - [b - 17]
√361 - 2(-3)² - [(4) - 17]
√361 - 2(9) - [4 - 17]
√361 - 18 - [-13]
√361 - 18 + 13
19 - 18 + 13
1 + 13
14
Given that a = -3 and b = 4, the numerical value of the expression (√361 - 2a² - [b - 17]) is 14.
Learn to solve more algebraic problems here: https://brainly.com/question/27122308
#SPJ1
The perimeter of any rectangle in which the length is 4 more than twice the width is P = 6 w + 8 , where w is the width. Which formula can be used to find the width given the perimeter? Multiple choice question. cross out A) w = P − 4 3 cross out B) w = 1 6 P − 8 cross out C) w = − P + 8 6 cross out D) w = P − 8 6
Answers
Answer: option D
Step-by-step explanation:
Given equation:
P = 6 w + 8 [eq1]
l=2w+4 [where l is length]
using eq1 we have:
6w=P-8
w=(P-8)/6
hence option D
learn more about perimeter here:
https://brainly.com/question/28499208
#SPJ9
Which did you include in your response?
The relation is a function if there is only one point of
intersection for any vertical line on the graph.
The relation is not a function if any vertical line has
more than one point of intersection on the graph.
The vertical line test is used to determine if one
input has exactly one output.
Answers
Use the vertical line test to determine whether a graph represents a function or not .
If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is a relation but not a function.
A function can only have one output, y, for each unique input, x. If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function.
what is function?
function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Therefore, a relation which maps a given input to more than one output is not a function, as such, given that the line intercepts the vertical line twice, then for a given value of x, which is the input, there are more than one value of y, which is the output, as such the relation is not a function.
To learn more about Functions
visit : brainly.com/question/11624077
#SPJ9
What are the solutions to this linear system?
Answers
Building systems of equations, we have that:
a) The price of a cow is of 1200 coins, the price of a sheep is of 500 coins and the price of a pig is of 300 coins.
b) The system of equations is composed by the equations given below.
x + 9 + 4 = 15.7 + y + z = 15.t + 1 + w = 15.x + 7 + t = 15.9 + y + 1 = 15.4 + z + w = 15.x + y + w = 15.4 + y + t = 15.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For item a, the variables are given as follows:
Variable x: Price of a cow.Variable y: Price of a sheep.Variable z: Price of a pig.Considering that a sell is positive money and a buy negative, and the text, the equations are given as follows:
2x + 5y - 13z = 1000.3x - 9y + 3z = 0.-5x + 6y + 8z = -600.Using a calculator, the solutions are given as follows:
x = 1200, y = 500, z = 300.
Hence:
The price of a cow is of 1200 coins, the price of a sheep is of 500 coins and the price of a pig is of 300 coins.
For item b, all missing values are variables, given by:
x, y, z, t and w.
From the sum of the rows:
x + 9 + 4 = 15.7 + y + z = 15.t + 1 + w = 15.From the sum of the columns:
x + 7 + t = 15.9 + y + 1 = 15.4 + z + w = 15.From the diagonals:
x + y + w = 15.4 + y + t = 15.The system is composed by all these equations.
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
You are choosing between two health clubs. Club A offers membership for a fee of plus $18 a monthly fee of $20 Club B offers membership for a fee of $12 plus a monthly fee of $23 After how many months will the total cost of each health club be the same? What will be the total cost for each club?
Please help thank you
Answers
Answer:
x=5
Step-by-step explanation:
so after five months, the costs would equal each other.
Explanation:
You'd have to write equations for the price per month for each club.
Let x equal the number of months of membership, and y equal the total cost. Club A's is y=25x+40 and Club B's is y=30x+15.
Because we know that the prices, y, would be equal, we can set the two equations equal to each other.
25x+40=30x+15.
We can now solve for x by isolating the variable.
25x+25=30x.
25=5x.
5=x
After five months, the total cost would be the same.
f(x) = -3x² - 2x
how to find f (8)
Answers
Answer:
f(8) = -208
Step-by-step explanation:
Apply 8 into the equation
f(8) = -3(8)² - 2(8)
= -192 - 16
= -208
8 will be your x value since it's implied within the question itself.
Answer:
-208
Step-by-step explanation:
Given function:
[tex]\text{f}(x)=-3x^2-2x[/tex]
To find f(8), substitute x = 8 into the function:
[tex]\begin{aligned}\text{f}(x) & =-3x^2-2x\\\implies \text{f}(8) & =-3(8)^2-2(8)\\& =-3(64)-2(8)\\& =-192-16\\& = -208\end{aligned}[/tex]
Therefore, f(8) = -208.
Bob is x years old. His brother, Matt, is 4 years older than Bob. Their aunt, Lana, is 5 years less than twice Matt’s age.
Write and simplify an expression that represents Lana’s age in years.
Answers
Answer:
9 9 years 9999999999999
Evaluate the expression when m= -4
m2 +6m +9
Answers
Answer: 36. Substitute: - 32 - 6 * - 3 + 9 Remove the parentheses: 32 + 6 * 3 + 9 Calculate the power:9 + 6 * 3 + 9.
Step-by-step explanation: I hope this help
Answer:
= 1
Step-by-step explanation:
m² + 6m + 9
m = -4
= -4² + 6*-4 + 9
= 16 -24 + 9
= 25 - 24
= 1
Are these a function or not? Will give BRAINLEIST
Answers
Answer:
D:function, E:not a function
Step-by-step explanation:
We can figure this out using the line test. To do the line test you draw multiple straight, vertical lines along the graph, and if at any point the figure in question touches one of the lines multiple times, that figure is not a function.
:D