The coefficient of [tex](x-2)^{4}[/tex] the fourth-degree Taylor polynomial for f about x=2 could be 7/12, 17/18, 3/8, or 3/4, depending on the value of f''''(2).
To find the coefficient of [tex](x-2)^{4}[/tex] the fourth-degree Taylor polynomial for f about x=2, we need to use the formula for the Taylor polynomial:
P4(x) = f(2) + f'(2)(x-2) + (1/2!)f''(2)[tex](x-2)^{2}[/tex] + (1/3!)f'''(2)[tex](x-2)^{3}[/tex] + (1/4!)f''''(2)[tex](x-2)^{4}[/tex]
We know that f'''(x) =[tex](4x-1)^{3/2}[/tex], so f'''(2) = [tex](4(2)-1)^{3/2}[/tex] = 27.
Substituting this value into the formula for the Taylor polynomial, we get:
P4(x) = f(2) + f'(2)(x-2) + (1/2!)f''(2)[tex](x-2)^{2}[/tex] + (1/3!)(27)[tex](x-2)^{3}[/tex] + (1/4!)f''''(2)[tex](x-2)^{4}[/tex]
We need to find the coefficient [tex](x-2)^{4}[/tex], so we can ignore all the other terms and focus on the last term:
(1/4!)f''''(2)[tex](x-2)^{4}[/tex]
The coefficient [tex](x-2)^{4}[/tex] is the coefficient of the fourth term in the expansion of [tex](x-2)^{4}[/tex], which is 1/(4!).
Therefore, the coefficient of [tex](x-2)^{4}[/tex] the fourth-degree Taylor polynomial for f about x=2 is:
(1/4!)(f''''(2)) = (1/24)(f''''(2))
Without knowing the value of f''''(2), we cannot determine the exact coefficient. However, we can provide the possible options:
- If f''''(2) = 14, then the coefficient of [tex](x-2)^{4}[/tex] is (1/24)(14) = 7/12.
- If f''''(2) = 34/3, then the coefficient of[tex](x-2)^{4}[/tex] is (1/24)(34/3) = 17/18.
- If f''''(2) = 9/2, then the coefficient of [tex](x-2)^{4}[/tex] is (1/24)(9/2) = 3/8.
- If f''''(2) = 18, then the coefficient of[tex](x-2)^{4}[/tex] is (1/24)(18) = 3/4.
In conclusion, the coefficient of[tex](x-2)^{4}[/tex] the fourth-degree Taylor polynomial for f about x=2 could be 7/12, 17/18, 3/8, or 3/4, depending on the value of f''''(2).
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Drag the red and blue dots along the x-axis and y-axis to graph
3x+8y=27
Answer:
Hope this helps you
Step-by-step explanation:
3x+8y=27 (0,9) .... look at picutre
helppp pls ive been here ages
The final velocity in the given equation is −0.5, when the acceleration is -5.
What is velocity?The distance covered by a body in one unit of time in a specific direction is referred to as velocity. M/s is always the only metric unit of velocity.
Speed and velocity are different in that:
i) velocity is a vector quantity, meanwhile speed is a scalar quantity.ii) Speed is always positive, in contrast to velocity, which can be either positive or negative.iii) The difference between velocity and speed is the amount of distance covered in a given amount of time when moving in a specific direction.v = u + at
here,
a = average acceleration
v = final velocity
u = initial velocity
t = time
given, u = 2
a = -5
t = 1/2 = 0.5
putting the values
v = 2 + (-5)(0.5)
v = 2 - 2.5
v = −0.5
Thus, The final velocity in the given equation is −0.5, when the acceleration is -5.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided Write a list of steps that are needed to find the measure of ∠B
The measure of angle B in the given triangle is 41°
Calculating the measure of an angle in a triangleFrom the question, we are to calculate the measure of angle B.
From the exterior angle theorem of a triangle which states that if a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
Then,
We can write that
∠B + 72° = 113°'
∠B = 113° - 72°
∠B = 41°
Hence, the measure is 41°
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Are there 360 or 361 longitudes?
There are 360 longitudes. Longitudes are imaginary lines that run vertically around the earth and measure distance east or west of the Prime Meridian.
There are a total of 360 longitudes, which are divided into 180 degrees east and 180 degrees west.
Longitudes are imaginary lines that run vertically around the earth and measure distance east or west of the Prime Meridian. This Prime Meridian is the reference point which divides the planet into two equal halves. There are a total of 360 longitudes, which are divided into 180 degrees east and 180 degrees west. The longitudes are also referred to as meridians and they are used to measure the exact location of any place on the earth's surface. This helps in navigation and also in mapping the world. Each meridian is assigned a numerical value, ranging from 0 degrees at the Prime Meridian to 180 degrees at the International Date Line. The longitudes are also used to calculate time zones, with 15 degrees representing one hour of time difference. Therefore, the total number of longitudes will always remain 360, no matter the size of the earth.
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Your friend Tammy just got a part-time job so she can afford to attend a school trip abroad later this school year. Tammy gets a paycheck on the 1st of every month, and a cash payment is due to the International Club advisor by the 3rd of every month with no exceptions. More than one late payment results in being removed from the trip. What recommendation do you have for Tammy?
I recommend that Tammy create a budget to keep track of her income and expenses. She should also set up automatic payments for her International Club advisor so she doesn't miss any payments. Additionally, Tammy should create a savings plan for the trip to make sure she has enough money for it. Finally, she should start the habit of setting aside money from each paycheck for the trip, so she has a consistent source of funds when she needs them.
Find the zeros of the polynomial: x 3+2x 2−x−2A1,−1,−2B1,3,7C1,−2,4DNone of these
The zeros of the polynomial x3 + 2x2 - x - 2 are -1, -2 and 4.
The given polynomial is x3 + 2x2 - x - 2. To find the zeros of this polynomial, we need to solve the equation x3 + 2x2 - x - 2 = 0.
Rewrite the equation as x3 + 2x2 - x - 2 = 0.
Factor the equation.
Set each factor equal to zero and solve for x.
(x + 2)(x2 - x - 1) = 0
x + 2 = 0
x = -2
(x2 - x - 1) = 0
x2 - x - 1 = 0
x2 - 1x - 1 = 0
Apply the quadratic formula to solve for x.
x = [-b ± √(b2 - 4ac)] / 2a
x = [(-1) ± √(1 - 4*1*(-1))] / 2*1
x = [(-1) ± √(5)] / 2
x = [-1 ± √5] / 2
x = [(-1 + √5) / 2] and [(−1 - √5) / 2]
Simplify the solutions and find the zeros of the polynomial.
x = (-1 + √5) / 2 and x = (-1 - √5) / 2
Therefore, the zeros of the polynomial x3 + 2x2 - x - 2 are -1, -2 and 4.
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Someone please answer this for me!
the answer is 22 only because I said so and that mean I’m right
Gabriel earns $11.25 per hour at his job. He also receives a bonus of $20 each week if he arrives on time for each of his shifts. Assuming Gabriel is always on time, and x is the number of hours he works, which rule for f(x) models his weekly paycheck?
his pay check equation will be f(x) = 11.25x + 20
12 sodas for 3.24 find the unit rate
Answer:
Step-by-step explanation:
0.27 is the answer
the diameter of a wheel is 3 feet. what is the distance around the wheel
Answer: 9.42 Feet or 9 Feet 5.04 Inches
Step-by-step explanation: To solve for the circumference, the equation you must use is C = 2πr (Circumference = 2pi(3.14)radius(half of the diameter)).
question is in picture below
Answer:
C
Step-by-step explanation:
[tex]-12<4x \leq 8 \\ \\ -3<x \leq 2[/tex]
Answer:
[C] x > -3 and x ≤ 2
Step-by-step explanation:
[tex]\mathrm{Given:}-9 < 4x+3\leq 11[/tex]
[tex]\mathrm{{If}\:a < u\le \:b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u\le \:b}[/tex]
[tex]-9 < 4x+3\quad \mathrm{and}\quad \:4x+3\le \:11[/tex]
[tex]\mathrm{solving\;the\;first\;one}:-9 < 4x+3[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]4x+3 > -9[/tex]
[tex]\mathrm{subtract\;3\;from\;both\;sides}:\\4x > -12[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}4\\\\\frac{4x}{4} > \frac{-12}{4}[/tex]
[tex]x > -3[/tex]
[tex]\mathrm{Now\;with\;the\;second\;one}:4x+3\le \:11[/tex]
[tex]\mathrm{subtract\;3\;from\;both\;sides}:\\4x\le \:8[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}4[/tex]
[tex]\frac{4x}{4}\le \frac{8}{4}[/tex]
[tex]x\le \:2[/tex]
Therefore, the answer is [C] x > -3 and x ≤ 2
RevyBreeze~
Help with question A.
To do simple subtraction, use the - (minus sign) arithmetic operator.
How to get a proper Conclusion?6N + 10
---------- - 5 =
2
3N + 5 - 5
3N
so yes, you will always get triple the original number. or 3N.
A final step should be to divide the last difference by 3, which gets you
the original number back.
Two positive integers added together are always positive.
When two negative integers are added together, the result is always negative.
The result of subtracting two positive integers might be either positive or negative.
The result of subtracting two negative integers might be either positive or negative.
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How do i make a study guide for graphing and functions HELP
Discuss the position of the Anti-Federalists related to ratification of the Constitution. Use facts.
The anti-federalist assumed that using the constitution will increase the oppression of the people by those in power but regardless, the constitution was ratified
What is Anti-FederalistThe Anti-Federalists were a group of individuals who opposed the ratification of the Constitution. They believed that the Constitution granted too much power to the central government and did not adequately protect the rights of individual states and citizens. They argued that the Constitution should include a bill of rights to safeguard individual liberties and that the government should be more closely modeled after the Articles of Confederation. Additionally, some Anti-Federalists believed that the Constitution would lead to the rise of an aristocracy and the oppression of the common people. Despite their opposition, the Constitution was ultimately ratified in 1788 with the support of Federalists.
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Which addition would MOST likely improve the effectiveness of the advertisement?
a picture of the pillow
a personal quote from someone who has used the pillow
research that verifies the number of people who preferred the pillow
a consumer safety rating
Answer:
Research that verifies the number of people who preferred the pillow.
Sorry, if I'm wrong.
What is the new substitution rule?
The new substitution rule states teams will be able to make five substitutes instead of the traditional three during each match.
Teams have decided to allow more substitutions after voting in favor of the change. Teams will now be permitted to use five substitutions instead of the customary three throughout each game starting in the 2022/2023 season.
The primary motivation for this choice is to lessen the negative impacts of increased match intensity and fixture congestion, which are thought to have a direct influence on player health and well-being. Over time, it will become clear how an increase in substitutes would affect player health and happiness.
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A student uses 4 cup of peanuts to make 3 cups of
Trail Mix. Using this same proportion, how many cups of
peanuts are needed to make 5 cups of Trail Mix?
Answer quickly I gotta finish my work asap
Answer:
6 [tex]\frac{2}{3}[/tex] cups
Step-by-step explanation:
we can set up a proportion:
[tex]\frac{4}{3}[/tex] = [tex]\frac{t}{5}[/tex] 't' equals the number of cups of peanuts to make 5 cups trail mix
now we can cross-multiply to get:
3t = 20
t = 20/3 or 6 2/3 cups
Use the point in the graph to find the equation of the line in point-slope form
A
y-3=5(x-1)
B
y+3=5(x+1)
C
y+3=5(x-1)
D
y-3=5(x+1)
Answer: the correct answer is A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The equation of the graph in the slope intercept form is
y = 5x -2
The slope is 5. If you start at the y-intercept (0, -2) and go up 5 and 1 to the right you will be at the red point (1,4). The slope is the rise over the run.
[tex]\frac{5}{1}[/tex] = 5.
The y -intercept is where the line crossed the y axis (0,-2)
The y intercept is -2
A
y - 3 = 5x - 5 Add 3 to both sides
y - 3 + 3 = 5x - 5 + 3
y = 5x -2
the toll on a highway us based on the miles driven. If the toll in a 15-mile stretch on a highway is $0.60. find the cost to drive a 80-mile stretch
Answer: $3.20
Step-by-step explanation:
We have
15-mile stretch = $0.60
80-mile stretch = x
Cross Multiply
15 × x = 80 × $0.60
x = 80 × $0.60/15
x = $3.20
Hence, the cost to drive an 80-mile stretch is $3.20
What is the value of x? round to the nearest tenth, if necessary. responses x = 4 x, = 4 x = 5 x, = 5 x = 6.2 x, = 6.2 x = 9.4
By Using Pythagorean Theorem, the value of x is 6.2 units.
Pythagorean Theorem:
In mathematics, the Pythagorean Theorem or Pythagorean Theorem is the fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of a square whose side is the hypotenuse (opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation for the lengths of sides a, b and hypotenuse c and is often called the Pythagorean equation.
a² +b² =c²
Now,
By using the Pythagorean theorem:
Hypotenuse² = Perpendicular² + Base²
Now,
In the Δ ABD
As given
DB² = DA² + AB²
As given
DB = 13 units
AB = 9 units
Putting values in the above
13² = 9²+ DA²
169 - 81 = DA²
88 = DA²
Now,
In ΔABC
AB² = AC² + CB²
(As given AB = 9 units , CB = x)
9² = AC² + x²
AC ² = 81 - x²
Now in ΔADC.
AD² = AC² + DC ²
As
AC ² = 81 - x²
DC = 13 - x
AD = [tex]\sqrt{88}[/tex]
(√88)² = 81 -x² +( 13 - x²)
By using the formula (a + b)² = a² + b² + 2ab
88 = 81 - x² + 13²- 2 × 13 × x + ²
⇒ 88 = 81 - x² + 13² - 26x + x²
⇒ 88-81 - 169 = -26x
⇒ 88-250 =-26x
⇒ -162 = - 26x
x = 6.2 (Approx.)
Therefore the value of x is 6.2 units.
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Farmer Dubble started with 87 elentires on
his farm. Every month, he exploded 5 more
of them. Farmer Gespil started with 13
elentires on her farm. Every month, she got
8 more of them.
Write a system of equations, in
slope-intercept form, to model each
farmer's elentires (y) as months (x)
increase.
The equations in the slope intercept form are,
y = -5x + 87
y = 8x + 13
What is slope intercept form?
The equation of the line can be written in different ways. One of the methods of writing equations of a line is slope intercept form.
The line with m as the slope, and c as the y-intercept is the graph of the linear equation y = mx + c. This form of linear equation is known as slope intercept form. The values of m and c are real integers in the slope-intercept form of the linear equation.
The slope, m, is a measure of how steep a line is. A line's y-intercept, c, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
For farmer Dubble,
Number of elentires in beginning c = 87
Number of elentires destroyed every month m = -5
Linear equation in slope intercept form
y = -5x + 87
For farmer Gespil,
Number of elentires in beginning c = 13
Number of elentires bought every month m = 8
Linear equation in slope intercept form
y = 8x + 13
Therefore the system of equations in slope intercept form are,
y = -5x + 87
y = 8x + 13
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If f(x)=x is the parent graph, then which equation represents the shown transformation?
y-axis 6 5 4 3 2 1 x=ax S 4 -3 2 -1 1 2 3 4 5 6 -1 -2.
What is transformation?It refers to the act, process, or instance of transforming or being transformed. Regarding transformative learning, Mezirow indicates learning occurs when there is a transformation in one of our beliefs or attitudes, or a change of our entire perspective. Learn more in: Connecting Teachers' Dispositions With Their Teaching Philosophies2.A process of change and development. When it refers to human transformation, it implies an internal change and growth to one’s highest potential or best oneself, which affects one’s worldview, behaviors, and thought. Learn more in: Two Languages, One Self: The Story of My Bilingual Journey3.In general it is a result of an effect of environment that changes an object. In everyday practice it is a set of actions that change the state or properties of different materials, goods, services or knowledge. Learn more in: Instructional Technologies of the XXI Century: Theoretical ApproachTo learn more about Theoretical Approach refer to:
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A transformation modifies the parent function's graph.
What is meant by Transformations?The graph of a parent function is changed by a transformation. Transformations come in three different flavors: translations, reflections, and dilations.
A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.
Making pictures or replicas of an object is part of transformation geometry. You are introduced to transformation geometry in grade 9 through the use of translation, reflection, dilation, and rotation.
The foundation of the problem transformation approach is the notion that, if we are unable to address the given problem directly, we will move it to a setting where we can do so. The method's fundamental component is how the problem is broken down into smaller tasks.
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A 10 1/2 -inch candle burns down in 6 hours. At what rate does the candle burn, in inches per hour?
Answer:
1 [tex]\frac{3}{4}[/tex] inches per hour
Step-by-step explanation:
10 [tex]\frac{1}{6}[/tex] ÷ 6
10.5 ÷ 6 = 1.75
1.75 is the same as 1 [tex]\frac{3}{4}[/tex]
Does 8cm 15cm and 17cm form a right triangle?
Answer:
No, the sides of a right triangle must obey the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 8^2 + 15^2 = 64 + 225 = 289, which is not equal to 17^2 = 289. Therefore, 8cm, 15cm, and 17cm do not form a right triangle.
Step-by-step explanation:
1
The graph shows an image of a dilation about the origin with a scale factor of 2.
-10-8-6-4-
2
40
1
What are the coordinates of the pre-image of A', point A?
(-8,-12)
01
8 10 X
As a result, the answer to the provided coordinate plane problem is only choice C), which is the right answer.
What is a coordinate plane?The term "coordinate plane" refers to a two-dimensional region that consists of two number lines. It emerges when the X-axis & Y-axis intersect at a location known as the origin. Using the numbers on a coordinate grid, one can locate points.
Here,
Since, If there is a coordinate plane with both parallel lines, go with option A.
Therefore, there is no cure.
There are hence a finite number of solutions that could be found.
If two lines cross, there is only one potential result for Option B. Consequently, the quantity of potential solutions is.
According to Option C, there must be an endless number of solutions to the system because there are two coinciding lines that provide us an infinite number of junction sites.
The difference between Option D) and Option B) is noted.
Only choice C) is hence the proper one.
Therefore , the solution to the given problem of coordinate plane comes out to be Only choice C) is hence the correct one.
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does anyone know this question ?? please help
Answer:
Step-by-step explanation:
the 3rd
How does the substitution method works for solving a two order system of equations?
The method of solving "by substitution" works by solving one of the equations for one of the variables, and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.
A quadratic equation is a second-order equation written as ax² + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
To solve two order system of equations using substitution, follow these steps:
Step 1. Choose one equation and solve it for either of the one variables.
Step 2. In the other equation, substitute the value get from step 1.
Step 3. Solve the new equation.
Step 4. Substitute the value found into any equation involving both variables and solve for the other variable.
Step 5. Check the solution in both original equations.
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Find the sum of the measures of the interior angles of a convex nonagon.
The sum of the measures of the interior angles is ?
answer
7π radians
steps
non in nonagon means 9
nonagon has 9 sides
convex means each angle is less than 180°
sum of interior angles convex N -sided polygon =
π(N −2) radians
π(9 −2) radians
7π radians
socratic
wikipedia
cuemath
mathworldwolfram
oxfordlanguages
Answer:
7πradians
Step-by-step explanation:
non in nonagon means 9
nonagon has 9 sides
convex means each angle is less than 180°
sum of interior angles convex N-sided polygon=
π(N-2) radians
π(9-2) radians=
7πradians
What is the exponential value of 3?
The exponential value of 3, also known as [tex]e^3[/tex] is the value of the mathematical constant e (approximately equal to 2.71828) raised to the power of 3.
To calculate [tex]e^3[/tex] , we would use the following formula:
[tex]e^3[/tex]= e x e x e = 2.71828 x 2.71828 x 2.71828 = 20.0855
So, the exponential value of 3 is approximately 20.0855.
It's important to note that the exponential value of any number is a real number, the value of e is raised to the power of that number. The mathematical constant e, also known as Euler's number, is an important number in mathematics and is used in various branches such as calculus, statistics and probability. It has also been used in physics and engineering, it appears naturally in many processes such as radioactive decay, natural growth and decay of populations, and more.
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Do the side lengths 9 12 and 15 form a right triangle?
The sides of lengths 9, 12 and 15 will form right angled triangle with 15 as hypotenuse.
We can check if the mentioned side form right angled triangle or not by checking the values through Pythagoras theorem. The hypotenuse will be 15 from mentioned sides, as it is longest. Now, writing the Pythagoras theorem.
Hypotenuse² = Perpendicular² + Base²
15² = 9² + 12²
Taking square on the right and left hand side of the triangle
225 = 81 + 144
Performing addition on Right Hand Side of the triangle
225 = 225
Since both sides of equation are equal, hence, right angled triangle can be formed.
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