"
Find the Taylor polynomial of degree 3 near x = 5 for the following function. y = x - 4
Answers
To find the Taylor polynomial of degree 3 for the function y = x - 4 near x = 5, we need to determine the derivatives of the function at x = 5 up to the third derivative.
The first derivative of y = x - 4 is simply 1, as the derivative of x is 1 and the derivative of -4 is 0. The second derivative is 0, as the derivative of a constant (in this case, -4) is always 0. The third derivative is also 0, as the derivative of 0 (the second derivative) is always 0.Since the second and third derivatives are both 0, the Taylor polynomial of degree 3 reduces to a polynomial of degree 1, which is just the first derivative evaluated at x = 5. Therefore, the Taylor polynomial of degree 3 for y = x - 4 near x = 5 is y = 1(x - 5) + (-4), which simplifies to y = x - 9.
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Related Questions
Cual es el tiempo que debe transcurrir para que un préstamo de $ 160.000 genere un interés de $ 15.000 a una tasa del 5,5% de interés simple.
Answers
Answer:
2 años.
Step-by-step explanation:
De la pregunta anterior, se obtuvieron los siguientes datos:
Principal (P) = $ 160,000
Intereses (I) = $ 15,000
Tasa (R) = 5,5%
Tiempo (T) =?
Así, podemos obtener el tiempo que tarda el préstamo de $ 160.000 en generar un interés de $ 15.000 a una tasa de interés simple del 5,5% de la siguiente manera:
I = PRT / 100
15000 = 160000 × T × 5.5 / 100
15000 = 880000 × T / 100
15000 = 8800 × T
Dividir ambos lados por 8800
T = 15000/8800
T = 1,7
T ≈ 2 años
Por lo tanto, tomará aproximadamente 2 años.
Find all linearly independent solutions and a general solution to the homoge-
neous linear equation:
L(D)y(x) = ((D
Differential Equations
Show all work
Answers
Therefore, the general solution to the homogeneous linear equation is given by: y(x) = c1e^(3x) + c2e^(5x) + c3e^(6x), where c1, c2 and c3 are constants that can be determined using the initial conditions, if given.
Given, L(D)y(x) = ((D - 3)(D - 5)(D - 6))y(x)
= 0
We have to find all linearly independent solutions and a general solution to the homogeneous linear equation.
First, we find the roots of the characteristic equation, which are (D - 3)
= 0, (D - 5)
= 0 and (D - 6)
= 0.
The roots of the characteristic equation are: D1 = 3, D2 = 5 and D3 = 6.
Now, we can write three linearly independent solutions:
y1(x) = e^(3x)y2(x)
= e^(5x)y3(x)
= e^(6x)
A homogeneous linear equation is an equation of the form L(y) = 0, where L is a linear differential operator and y is a function of a single variable x. In general, the solutions to a homogeneous linear equation form a vector space, which means that any linear combination of solutions is also a solution.
The dimension of this vector space is equal to the order of the differential equation and the number of linearly independent solutions.
In other words, the number of linearly independent solutions is equal to the order of the differential equation.
To find the general solution to a homogeneous linear equation, we first find the roots of the characteristic equation, which is obtained by replacing the differential operator by its corresponding polynomial equation.
The roots of the characteristic equation are used to write down the linearly independent solutions, which can then be combined to obtain the general solution.
The constants of integration in the general solution are determined using initial or boundary conditions, if given.
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The position (in meters) of a particle moving along a straight line is given by s(t)=5t2−8t+13, where t is measured in seconds.What is the average velocity on each of the given unit time intervals? ANSWERED
[3,4]= 27 [4,5]= 37
Answers
The average velocity for the [3,4] is 27m/s and for [4,5] is 37m/s
The average velocity can be found by taking the derivative of the position function and evaluating it at the midpoint of the interval.
The average velocity on the interval [3,4] is given by (s(4) - s(3)) / (4 - 3), which is equal to (s(4) - s(3)) / 1. Using the position function, s(t) = 5t^2 - 8t + 13, we find that s(4) = 5(4²) - 8(4) + 13 = 61 and s(3) = 5(3²) - 8(3) + 13 = 34. Therefore, the average velocity on the interval [3,4] is (61 - 34) / 1 = 27 m/s.
The average velocity on the interval [4,5] is given by (s(5) - s(4)) / (5 - 4), which is equal to (s(5) - s(4)) / 1. Using the position function, s(t) = 5t² - 8t + 13, we find that s(5) = 5(5²) - 8(5) + 13 = 98 and s(4) = 5(4²) - 8(4) + 13 = 61. Therefore, the average velocity on the interval [4,5] is (98 - 61) / 1 = 37 m/s.
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In parallelogram LMNO, what is the measure of angle N?
50°
70°
110°
130
Answers
The measure of the angle N is equal to 110 degrees
What is a parallelogram?
A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
we know that
In a parallelogram opposite angles are congruent and consecutive angles are supplementary.
So
m∠O=m∠M
m∠L=m∠N
m∠O+m∠L= 180
Step
Find the value of x
(x+20)+(2x+10)=180
3x=150
x=150/3 = 50 degrees
Step
Find the value of angle L
m∠L = 2x+10
m∠L=2*50+10
m∠L=110 degrees
Remember that
m∠N=m∠L = 110 degrees
m∠N= 110 degrees
therefore
the answer is
the measure of the angle N is equal to 110 degrees
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Can you help me with this
Answers
Step-by-step explanation:
what we see on the left side is that both terms contain (y + 6).
so, the left side is actually
(y + 6) × (x - 5)
therefore,
(x - 5)
is the missing factor on the right side.
Find an antiderivative F(x) with F′(x)=f(x)=4+15x2+15x4 and F(1)=0.
Remember to include a "+ C" if appropriate.
F(x)=
Answers
The antiderivative of the function is F(x) = 4x + 5x^3 + 3x^5 - 12.
To find the antiderivative F(x) for F′(x) = f(x) = 4 + 15x^2 + 15x^4, and given F(1) = 0, follow these steps,
1. Find the antiderivative of f(x) with respect to x:
F(x) = ∫(4 + 15x^2 + 15x^4) dx
2. Integrate each term separately:
F(x) = ∫4 dx + ∫15x^2 dx + ∫15x^4 dx
3. Calculate the antiderivatives:
F(x) = 4x + (15/3)x^3 + (15/5)x^5 + C
4. Simplify:
F(x) = 4x + 5x^3 + 3x^5 + C
5. Use the given condition F(1) = 0 to find the value of C:
0 = 4(1) + 5(1)^3 + 3(1)^5 + C
6. Solve for C:
C = -12
7. Substitute the value of C back into F(x):
F(x) = 4x + 5x^3 + 3x^5 - 12
The antiderivative is F(x) = 4x + 5x + 3x - 12 as a result.
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The two-way table given shows the results from a survey of pet owners.
Owns a Dog Does Not Own a Dog Total
Owns a Cat 126 45 171
Does Not Own a Cat 54 15 69
Total 180 60 240
Does the data show an association between owning a dog and owning a cat?
There is a strong, positive association.
There is a strong, negative association.
There is a weak, negative association.
There is a weak, positive association.
Answers
From the total amounts, the correct option regarding the association between owning a dog and owning a cat is given by:
There is a strong, positive association.
What are positive and negative association between amounts?If there is a positive association, both behave similarly, that is, either both increase and both decrease simultaneously.If there is a negative association, both behave inversely, that is, one amount decreases and the other increases.Whether the association is strong or weak depends on the rate of change, the rate of increase or decrease.
From the amounts in the table, we have that:
126 own both a cat and a dog, 15 own neither.45 own a cat but not a dog, 54 own a dog but not a cat.Having a cat increases the likelihood of having a dog and vice-versa, hence there is a strong, positive association and the first option is correct.
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Which table shows a function that is decreasing over the interval (-2, 0)?
x
f(x)
f(x)
X
f(x)
-2
0
-2
-15
-3
N
-1
-5
0
-5
-2
0
0
0
2.
-20
-1
-10
1
5
4
4
-30
0
-24
O
O
Answers
Answer:
it is becoming a actual number and not a negative
Sarah purchased 8kg of sugar, 10kg of
flour, 500g of cocoa, 225g of pecans,
and 275g of coconut. How much do all
her groceries weigh in kilograms?
Answers
The total weight is 18.5 kilograms
Find the slope of the tangent line to the graph at the given point. witch of agnesi: (x2 4)y = 8 point: (2, 1)
Answers
The slope of the tangent line to the witch of Agnesi graph at the point (2, 1) can be found by taking the derivative of the equation and evaluating it at the given point. The slope is 1/2 .
The equation of the witch of Agnesi curve is given by (x^2 + 4)y = 8. To find the slope of the tangent line at a specific point on the curve, we need to take the derivative of the equation with respect to x.
Differentiating the equation implicitly, we get:
2xy + (x^2 + 4)dy/dx = 0.
To find the slope of the tangent line at a particular point, we substitute the x and y coordinates of that point into the derivative expression. In this case, we substitute x = 2 and y = 1:
2(2)(1) + (2^2 + 4)dy/dx = 0.
Simplifying the equation, we have:
4 + (4 + 4)dy/dx = 0,
8dy/dx = -4,
dy/dx = -4/8,
dy/dx = -1/2.
Therefore, the slope of the tangent line to the witch of Agnesi graph at the point (2, 1) is -1/2, or equivalently, -0.5.
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Complete the inequality. 13/18___ 11/14 < > =
Answers
Answer:
Your answer is <, Hope it helps.
What is the probability that a hand of 5 cards chosen randomly and without replacement from a standard deck of 52 cards (which has 4 kings and 4 queens) contains the king of spades, exactly 1 other king, and exactly 2 queens
Answers
Answer: Approximately 0.0003047
As a fraction, it is equal to exactly 792/(2,598,960)
===========================================================
Explanation:
The king of spades must be in the hand, and we can pick any other king. There are 3 ways to pick the other king. Then there are 4 C 2 = 6 ways to pick the two queens. The 4C2 refers to the nCr notation. Or you could use Pascal's Triangle.
Overall, there are 3*6 = 18 ways to pick the king of spades, another king, and exactly 2 queens.
Then we have one more card to pick that isn't a king nor a queen. There are 4+4 = 8 cards that are either a king or queen, leaving 52-8 = 44 cards that are neither.
So there are 18*44 = 792 ways to pick a king of spades, another king, exactly 2 queens, and some other card that isn't a king nor queen.
This is out of 52C5 = 2,598,960 possible five card hands.
The probability we're after is roughly 792/(2,598,960) = 0.0003047
Side note: order does not matter with card hands.
Without graphing, determine whether the function represents exponential growth or exponential decay.
y = 129(1.63)x
Answers
The exponential growth of three sections is given below.
What is exponential growth?Exponential growth means whose growth more rapid in proportion.
An exponential function is of the form , where b is a positive number not equal to 1.
The value of b determines whether tha function is an exponential growth or an exponential decay.
An exponential function is an exponential growth if b > 1 and an exponential decay if b <1.
Given the function= y 4(5/6)^x
B= 5/6 < 1
Therefore, the function is an exponential decay.
Given the function
Therefore, the function is an exponential growth.
Therefore, the function is an exponential growth is y= 129(1.63)^x is an exponential growth.
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why is the term ""arc"" used to describe units of measure for angular distance
Answers
The term "arc" is used to describe units of measure for angular distance because it refers to the length of an arc on a circle.
Angular distance is the measure of the separation between two points on a circle or an arc. The term "arc" is used to describe this measure because it refers to the length of the arc connecting the two points on the circle.
This length is a fraction of the circumference of the circle and is proportional to the angle between the two points. The use of the term "arc" in this context is a nod to the geometric origins of angular measurement, which is based on the properties of circles and their angles.
The most common units of angular measurement are degrees, minutes, and seconds, which are all based on the division of a circle into 360 equal parts (degrees) and further subdivisions (minutes and seconds).
Other units of angular measurement, such as radians and gradians, are also based on the properties of circles and their angles.
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Practice Problem F р You took Loan of 5000 for 24 months on 1% per month, 1- Find A = 23.55 2- Find the interest and principal in the 7th payment?
Answers
1- A = 23.55
2- In the 7th payment, the interest is $50 and the principal is $193.55.
To find the value of A, we can use the formula for calculating the monthly payment on a loan. Given that you took a loan of $5000 for 24 months at an interest rate of 1% per month, we can substitute these values into the formula. By doing so, we find that A is equal to $23.55.
To determine the interest and principal in the 7th payment, we need to understand how loan payments are typically structured. Each monthly payment consists of both interest and principal components. Initially, the interest portion is higher, while the principal portion gradually increases over time.
In this case, we know the loan amount is $5000, and the loan term is 24 months. To find the interest and principal in the 7th payment, we need to calculate the remaining balance after the 6th payment.
To calculate the remaining balance after the 6th payment, we subtract the total amount paid from the initial loan amount. The total amount paid after 6 payments can be calculated by multiplying the monthly payment (A) by the number of payments (6). In this case, 6 * $23.55 equals $141.30.
Next, we subtract the total amount paid ($141.30) from the initial loan amount ($5000) to get the remaining balance, which is $4858.70.
Now, we can calculate the interest in the 7th payment. Since the interest rate is 1% per month, the interest for the 7th payment can be found by multiplying the remaining balance ($4858.70) by 1% (0.01), resulting in $48.59. Therefore, the interest in the 7th payment is $48.59.
To find the principal in the 7th payment, we subtract the interest ($48.59) from the monthly payment ($23.55). This gives us $174.96. However, we need to adjust the principal amount to match the remaining balance after the 6th payment. Therefore, we subtract the remaining balance after the 6th payment ($4858.70) from $174.96 to find the adjusted principal, which is $193.55.
In summary, in the 7th payment, the interest is $48.59 and the principal is $193.55.
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Lin counts 5 bacteria under a microscope on the first day
She counts them again each day and finds that the number of bacteria doubled
each day—from 5 to 10, then from 10 to 20, and so on.
Given that the number of bacteria is a function of time (the number of days), how many bacteria exist on the 6th day
Answers
30 is the answer
Step-by-step explanation:
5 10 15 20 25 30
or 5x6
Delilah has assets that total $56,326 and liabilities that total $32,129. What is her net worth?
Answers
The net worth of Delilah given the assets and liabilities will be $24197.
How to calculate the net worth?From the information given, Delilah has assets that total $56,326 and liabilities that total $32,129.
It should be noted that the formula to calculate the net worth will be:
= Assets - Liabilities
= $56,326 - $32,129
= $24197
The net worth is $24197.
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Please Help me answer all 4 questions with a full explanation so I can solve the rest on my own.
Answers
\(\\ \rm\Rrightarrow (2x^2)^3.2yx^0=8x^6.2y=16x^6y\)
\(\\ \rm\Rrightarrow (2x^4y^3)^3.2x^4y^4=8x^{12}y^6.2x^4y^4=16x^{16}y^{10}\)
\(\\ \rm\Rrightarrow (m^3n^0(2m^3n^2)^4)^2=(m^316m^{12}n^8)^2=(16m^{15}n^8)^2=256m^{30}n^{16}\)
\(\\ \rm\Rrightarrow (2xy^3)^2.2x^2y^0=4x^2y^6.2x^2=8x^4y^6\)
What are the 4 tests for similar triangles?
Answers
The 4 tests for similar triangles are:-
AAA: Three pairs of equal angles.
SSS: Three pairs of sides in the same ratio.
SAS: Two pairs of sides in the same ratio and an equal included angle.
ASA: Two angles and the side included between the angles of one triangle are equal
What is AAA,SAS,ASA,SSS?
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.
According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.
According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.
According to the AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."
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The total number of fans is attendance at a Wednesday baseball game was 48,268. The game had 12,568 more fans than the Tuesday game the day before. How many fans attended each game?
Answers
35,700+48,268=83,969.
Write an equation to represent the following statement.
The product of 7 and j is 91
Answers
Answer: 7j = 91
CORRECT ME IF I'M WRONG!
Hope this helps!
Brainliest would be great!
Answer:
7(j)=91
j=13
Step-by-step explanation:
Trust me on this one.
I multiplied 13 and 7 that equals 91.
1.3: Seagulls Soar, Sharks Swim
How far above or below sea level is each animal?
Measure to their eye level and approximate to the
nearest meter.
Answers
The table showing the distance of the animals from the sea level is as follows:
Animal - vertical position (meters) - seal level
Seagull - 10 m - above the sea level
Dolphin - 2.5 m - above
Penguin - 0 m - on the x-axis (sea level)
Shark - 4 m - below
Fish - 9 m - below
Octopus - 10 m - below
How the distance is measured from the coordinate axes?Here in the given graph, the animals are shown on the x-axis. I.e., the sea level and its movement (above or below) are shown on the y-axis.
The negative y-coordinates represent below the sea level and the positive y-coordinates represent above the sea level.
Thus, the distance from the sea level (on the x-axis) is shown on the y-axis in meters of the given animals as follows:
Seagull is 10 meters above the sea levelDolphin is 2.5 meters above the sea levelPenguin is lying on the x-axis, which means on the sea level neither above nor belowThe shark is 4 meters below the sea levelFish is 9 meters below the sea levelOctopus is 10 meters below sea level.Learn more about coordinate axes here:
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Write ways to represent the fraction 10/9.
Answers
Answer:
mixed number form 1 1/9
decimal form 1.11111111111111 it goes on forever
percent form 111.111111111111% it goes on forever (again)
Step-by-step explanation:
i hope that helps!
Answer:
1 1/9
Step-by-step explanation:
10/9, you get 1 as the whole number.
You have a 1 left over when dividing 10 and 9. the 1 will be over 9.
Giving you 1 as the whole number and 1/9 next to it.
I am trying to solve the equation; 2(x-2/3)=0. I need to show my work.
Answers
Answer:
x=−1
x=
2
3
=1
2
1
=1.5
Step-by-step explanation:
Answer:
x = 1/3
Step-by-step explanation:
The equation is : \(2(x-\frac{2}{3})\) = 0
Open parenthesis
\(2x - \frac{4}{6} = 0\)
Add 4/6 on both sides
2x = 4/6
Divide by 2 on both sides to isolate x
x = 1/3
Hope this helps :)
Have an awesome day!
Identify the antecedent and the consequent for each of the following conditional sentences. Assume that a, b, and f represent some fixed sequence, integer, or function, respectively.
(a) If squares have three sides, then triangles have four sides.
(b) If the moon is made of cheese, then 8 is an irrational number.
(c) b divides 3 only if b divides 9.
(d) The differentiability of f is sufficient for f to be continuous.
(e) A sequence a is bounded whenever a is convergent.
(f) A function f is bounded if f is integrable.
(g) 1 + 2 = 3 is necessary for 1 + 1 = 2.
(h) The fish bite only when the moon is full.
(i) A time of 3 minutes, 48 seconds or less is necessary to qualify for the Olympic team.
Answers
(a) Antecedent: Squares have three sides
Consequent: Triangles have four sides
(b) Antecedent: The moon is made of cheese
Consequent: 8 is an irrational number
(c) Antecedent: b divides 3
Consequent: b divides 9
(d) Antecedent: The differentiability of f
Consequent: f is continuous
(e) Antecedent: A sequence a is convergent
Consequent: a is bounded
(f) Antecedent: A function f is integrable
Consequent: f is bounded
(g) Antecedent: 1 + 2 = 3
Consequent: 1 + 1 = 2
(h) Antecedent: The moon is full
Consequent: The fish bite
(i) Antecedent: Time of 3 minutes, 48 seconds or less
Consequent: Qualification for the Olympic team
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Eight less than a third of a number is the sum of that number and one.
Answers
Answer:
\(x = -13\frac{1}{2}\)
Step-by-step explanation:
Eight less than a third of a number is the sum of that number and one.
Let the number be x.
That is:
\(\frac{1}{3}x - 8 = x + 1\\ \\=> x - \frac{1}{3}x = -8 - 1 \\\\\frac{2}{3}x = -9\\\\x = -9 * \frac{3}{2}\\ \\x = \frac{-27}{2}\)
\(x = -13\frac{1}{2}\)
Daniel is playing a video game. He has 7,985 points at the end of round one, then the following events happen, in order: • He doubles his points. • He loses 3,500 points. • He earns 4,972 additional points. • The game ends.
Answers
Starting points = 7,985
Doubling the points: 7,985 x 2 = 15,970
Subtracting 3,500 points: 15,970 - 3,500 = 12,470
Adding 4,972 points: 12,470 + 4,972 = 17,442
Therefore, Daniel has 17,442 points at the end of the game.
assuming iq scores are normally distributed, with a mean of 100 and a standard deviation of 15. what percentage of test takers could you expect to score 115 or higher?
Answers
Answer:
16%
Step-by-step explanation:
1) Mean, u = 100
standard deviation, o = 15
Score specified = x = 115
so, z-score = (x - u)/o
= (115 - 100)/15 = 1
From the probability standard normal distribution curve, 84.13% of the test scores falls within 1 SD (z score = 1), so, the percentage of test scores below 115 is 84.13%, so, for the percentage of test scores of 115 or higher = 100% - 84.13% = 16%.
Therefore, the correct answer is 16%.
help please and thanks !!
Answers
Answer:
Step-by-step explanation:
I think you put it in the middle
Erik and Nita are playing a game with numbers. In the game, they each think of a random number from 0 to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins. Use the information in the interactive and what you know about absolute value inequalities to better understand the game.
Answers
Question:
Write an algebraic statement that represents all the ways your player will win. Be sure to define your variable
Answer:
Erica:
\(0 \leq |x - y| < 10\)
Nita:
\(10 < |x - y| \leq 20\)
Step-by-step explanation:
Given
Players: Erica & Nita
Range: 0 to 20
Represent Erica with x and Nita with y
For Erica to win;
The difference between x and y must be less than 10 but greater than or equal to 0
i.e.
\(0 \leq x - y \leq 10\) or \(0 \leq y - x \leq 10\)
These two expressions can be merged together to be:
\(0 \leq |x - y| < 10\)
For Nita to win;
The difference between x and y must be greater than 10 but less than or equal to 20
i.e.
\(10 < x - y \leq 20\) or \(10 < y - x \leq 20\)
These two expressions can be merged together to be:
\(10 < |x - y| \leq 20\)