To find the maximum possible value of the error between the Maclaurin polynomial T3 of f(x) = e^x and the function value at x = 1.8, we need to use the Error Bound formula. The formula states that the absolute value of the error, |f(x) - Tn(x)|, is less than or equal to the maximum value of the nth derivative of f(x) times the absolute value of (x - a) raised to the power of n+1, divided by (n+1)!.
For the given function f(x) = e^x and Maclaurin polynomial T3, we have n = 3 and a = 0. The nth derivative of f(x) is also e^x. Substituting these values into the Error Bound formula, we get:
|f(x) - T3(x)| ≤ (e^c) * (x - 0)^4 / 4!
where 0 < c < x. Since we need to find the maximum possible value of the error for x = 1.8, we need to find the maximum value of e^c in the interval (0, 1.8). This maximum value occurs at c = 1.8, so we have:
|f(1.8) - T3(1.8)| ≤ (e^1.8) * (1.8)^4 / 4!
Rounding this to four decimal places, we get:
If(1.8) - T3(1.8) < 0.0105
The maximum possible value of the error between f(x) = e^x and its Maclaurin polynomial T3 at x = 1.8 is 0.0105. This means that T3(1.8) is a very good approximation of f(1.8), with an error of less than 0.011.
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t^2-4k+1=5
Solve by completing the square.
The solution of the quadratic equation k² - 4k + 1 = 5 will be 2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
k² - 4k + 1 = 5
Simplify the equation, then we have
k² - 4k + 1 = 5
k² - 4k - 4 = 0
Factorize the equation, then we have
k² - 4k - 4 = 0
k² - 2k - 2k - 4 = 0
k(k - 2) - 2(k - 2) = 0
(k - 2)(k - 2) = 0
k = 2, 2
The solution of the quadratic equation k² - 4k + 1 = 5 will be 2.
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The correct equation is given as,k² - 4k + 1 = 5
The sum of two numbers is 27. The difference between the two numbers is 5. What are the two numbers?
Answer:
x = 16
y = 11
Step-by-step explanation:
x+y = 27
x-y = 5
__________
2x = 27+5
2x = 32 /:2
x = 16
16+y = 27
y = 27-16
y = 11
Is it possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm Why or why not?
We cannot construct a triangle with side lengths 3.5 cm, 9.2 cm and 5.3 cm. So it is not possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm. This is because these lengths does not follow triangle inequality theorem.
It is not possible to construct a triangle using the given side lengths of 3.5 cm, 9.2 cm, and 5.3 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, if we take 3.5 cm and 5.3 cm as two sides, the sum of their lengths is 8.8 cm. But the length of the third side (9.2 cm) is greater than 8.8 cm, so these three side lengths cannot form a triangle.
It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle.
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What are the 4 different types of bar graphs?
The four types of bar graphs as follows:
Vertical Bar Graph.
Horizontal Bar Graph.
Grouped Bar Graph.
Stacked Bar Graph.
Rectangular bars are used in the particular type of data visualisation known as a bar graph, with the length of each bar matching to the value it represents. With the aid of rectangular bars that display the data's measure, the provided data is shown vertically in a graph or chart in a vertical bar graph. These graphs are referred to as horizontal bar graphs when the offered data is shown horizontally using rectangular bars that display the data's measure. These graphs are referred to as horizontal bar graphs when the offered data is shown horizontally using rectangular bars that display the data's measure.
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what is the slope of the graph?
The slope of the line is -4.
What is slope?A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). The slope is calculated as the ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two sites. A line's steepness is indicated by its slope. The slope's steepness increases with its size. The slope flattens out as it grows smaller. Slope also reveals whether a line is horizontal or vertical, or if it is going up or down. The slope in mathematics is a measure of how steep a line is. The gradient is another name for it. The slope equations.Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
From the diagram, the graph passes through point ( 0,2) and (1,-2)
Point 1( 0.2 )
x₁ = 0
y₁ = 2
Point 2( 1,-2 )
x₂ = 1
y₂ = -2
To determine the slope of the line, plug the coordinates into the above slope formula.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( -2 - 2 )/( 1 - 0 )
Slope m = ( -4 )/( 1 )
Slope m = -4/1
Slope m = -4
Therefore, the slope of the line is -4.
Option A is the correct answer.
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Hi, please help with this circle geometry question (image attached)! It would be helpful if you show your working out/proof. You also need to use tangent properties of circles.
Thank you!
Given that ABC is a right-angled triangle and that AB, BC, and CA are tangents to the circle, the value of x is 2 cm.
what is triangle ?Since a triangle has three parts and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to one triangle that has vertex shader A, B, and C. When the three principles are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sections and three corners. The points where the sides meet are known as the triangle's corners.
given
To find : radius 'r' of the incircle.
ABC is a right angled triangle
=100
⇒ BC= 100 =10cm
Since area of right anged triangle = 1/2×base×height
⇒ Area of △ABC= 1/2×6×8
=3×8=24cm 2
⇒ Area of △ABC=24cm 2 ....(1)
Also, Area of △ABC= area of △OAC+ area of △OBC+ area of △OBA
= 1/2 ×r×8+ 1/2 ×r×10+ 1/2 ×6×r= 1/2* r(8+10+6)= 1/2r(24)=12r....(2)
Equating (1) and (2) 12r=24
⇒ r= 12/24 =2cm
Given that ABC is a right-angled triangle and that AB, BC, and CA are tangents to the circle, the value of x is 2 cm.
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The complete question :- In fig. 4 triangle ABC is a right triangle with AB=6 cm, AC=8 cm and ∠A=90∘ . A circle with center O is inscribed inside the triangle. Find the radius 'r'
Raymond owns a used pickup truck that he wants to sell. A use-vehicle guide shows that its average retail value is $17,600. He adds $1,700 for 4-wheel drive, $475 for an entertainment system, $800 for a special trim package, and $225 for power locks. He also adds $125 for a sliding rear window, $325 for a towing package, $250 for power windows, and $3,125 for a diesel engine. He deducts $675 for having a manual transmission. He adds $450 for having less than the expected mileage. What is the average retail price of Raymond's vehicle?
The average retail price of Raymond's vehicle is $24,400.
What is Average Retail Price?
Average price is a measure of a range of prices. It is calculated by taking the sum of the values and dividing it by the number of prices being examined. The average price reduces the range into a single value, which can then be compared to any other point to determine if the value is higher or lower than what would be expected.
average retail value = $17,600
All the additions to the average retail value are;
$1,700 for 4-wheel drive
$475 for an entertainment system
$800 for a special trim package
$225 for power locks
$125 for a sliding rear window
$325 for a towing package
$250 for power windows
$3,125 for a diesel engine
$450 for less than expected mileage
Deductions
$675 for having a manual transmission
Average retail price = Average retail value + additions - deductions
Average retail price = $17,600 + ($1,700+$475+$800+$225+$125+$325+$250+$3,125+$450) - $675
Average retail price = $17,600 + $7,475 - $675
Average retail price = $24,400
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Help Please! I need to find the value of x in the quadrilateral
I know the sum of the exterior angles and interior angles is 360 and I know I need to do something with substitution but I have no idea where to start. Please explain it step by step so I understand.
The value of x in the quadrilateral is 23.
How to find the angles of a quadrilateral?A quadrilateral is a polygon with 4 sides. The sum of interior angles in a quadrilateral is 360 degrees.
The sum of exterior angles in a quadrilateral is 360 degrees.
Therefore, let's find the value of x in the quadrilateral.
Hence,
6x + 5x + x + 16 + 3x - 1 = 360
combine like terms
6x + 5x + x + 3x + 16 - 1 = 360
15x + 15 = 360
subtract 15 from both sides of the equation
15x = 360 - 15
15x = 345
divide both sides by 15
x = 345 / 15
x = 23
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You buy 1 bag of cat litter and 4 bags of
treats online for a total of $21. A few weeks later, you buy 2 bags of the same
cat litter and 8 bags of the same treats for a total of $42. Find the price of
each bag of litter and each bag of treats.
An electric car battery, when fully charged, can travel 520 miles. As the car travels, the charge decreases at a rate of 89 miles every 1 hour.
Enter an equation in slope-intercept form or y = mx + b that shows the amount of battery charge y, in miles, after traveling for x hours.
Answer:
The car can only last for 5 hours.
That's the answer I got.
5.84269662
Step-by-step explanation:
Alright so say I was driving for 2 hours I would have,
342 miles left.
If I were driving for 3 hours I would have,
253 miles left.
If I were driving for 4 hours I would have,
164 miles left.
Now if I were driving for 5 hours I would have,
75 miles left.
Statistics not sure if I did it right and I don’t understand the blank ones can someone please help?
A 95% confidence interval has a 0.95 probability of containing the population mean. 95% of the population distribution is contained in the confidence interval.
Does confidence interval mean probability?[tex]$p=\frac{17}{125}=.130$[/tex]
[tex]$2=\frac{.136-.15}{.03^2}$[/tex]
[tex]$(-4 a,=0.44)$[/tex]
This is the range of values that, with a certain degree of confidence, you would anticipate your estimate to fall within if you repeated your test. Another approach to describe probability in statistics is confidence. An interval of confidence shows the likelihood that a parameter will fall between two values close to the mean.
Measured by confidence intervals, the level of a sampling technique's uncertainty or certainty. Both regression analysis and hypothesis testing make use of them. As a typical method for estimating intervals, confidence intervals are frequently utilized. It's possible that if you've ever used this method, you've run into the following statement: For a 90% confidence interval, there is a 90% possibility that a real parameter resides within that interval.
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Find the volume of a pyramid with a square base, where the side length of the base is 19. 3\text{ ft}19. 3 ft and the height of the pyramid is 16. 2\text{ ft}16. 2 ft. Round your answer to the nearest tenth of a cubic foot.
The volume of the square pyramid is 2011.4 ft². The result is obtained by multiplying the area of base by height of the pyramid, then dividing it by 3.
What is the volume of a pyramid?
A pyramid is a polyhedron that has one base and lateral faces with the vertex at the top of the pyramid. The shape of lateral faces is always a triangle. While, the shape of the base varies and is used to name the pyramid.
The volume of the pyramid can be expressed as
V = ⅓ Bh
Where
B = area of baseh = height of a pyramidA pyramid with a square base has the side length of base of 19.3 ft. The height of the pyramid is 16.2 ft. Find the volume of the pyramid!
The area of base is
B = s²
B = 19.3 × 19.3
B = 372.49 ft²
The volume of the pyramid is
V = ⅓ Bh
V = ⅓ (372.49 ft²) (16.2 ft)
V = ⅓ (6034.338) ft²
V = 2011.446 ft²
V ≈ 2011.4 ft²
Hence, the volume of the pyramid with a square base is 2011.4 ft².
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PLS HELP LINE OF BEST FIT
From the linear function, at 50 degrees, the seller will sell 58 hot dogs, at 114 degrees, she will sell 35 hot dogs and from the line of best fit she will sell 3 hot dogs at every 10 degrees rise in temperature
What is Linear FunctionWhen plotted, a linear function is a sort of mathematical function that visually displays a straight line. A formula of the form y = mx + c, where m is the line's slope and c is its y-intercept, is used to describe it.
The linear function given is;
y = (3/10)x + 8
Where;
x = Temperature y = number of hot dogs solda) At 50 degrees, the number of hot dogs
Substituting the values into linear function;
y = 3/10(50) + 8
y = 150 / 3 + 8
y = 50 + 8
y = 58
The seller will sell 58 hot dogs at 50 degree
b) The temperature at which they will sell 35 hot dogs is;
y = (3/10)x + 8
35 = 3/10(x) + 8
35 * 10 = 3x + 8
350 = 3x + 8
3x = 350 - 8
3x = 342
x = 342 / 3
x = 114
The temperature at which they'll sell 35 hot dogs is 114 degrees
c) Based on the line of best-fit, for every 10 degree rise in temperature, she will sell 3 hot dogs.
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Draw a rectangle with 45 square units
Answer:
See below
Step-by-step explanation:
Here is one possibility:
Answer:easy
Step-by-step explanation:
I NEED URGENT HELP! 15 POINTS!
Jane had 27 stickers two weeks ago. Then she bought the same numbers of stickers each day for two weeks. Now she has 237 stickers. How many stickers did Jane buy each day?
Simplify: a) (−2)5x(−2)-3
2×2
Answer:
20x -64
Step-by-step explanation:
(−2)5x(−2)-3 2×2
2x5x x2-32x2
20x-32 x 2
20x -64
Write an equation of the line that passes through the given point and is parallel to the given line
The equation of the line that is parallel to 3y - x = - 12 and passes through (18, 2) will be 3y - x + 12 = 0.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.
The equation is given below.
3y - x = - 12
The equation of the line that is parallel to the given line is given as,
3y - x + d = 0
The equation that passes through (18, 2) will be given as,
3(2) - 18 + d = 0
6 - 18 + d = 0
d = 18 - 6
d = 12
Then the equation of the parallel line will be 3y - x + 12 = 0.
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A computer coast $800 it loses 1/5 of its value every year after it’s purchased complete the table after how many years will the computer be worth less than $100 _____ years write an equation representing the value v of the computer t years after it was purchased
On solving the provided question, we can say that equation for the question will be (n - 1) x 3/4
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
equation for the question will be
(n - 1) x 3/4
Value of the computer
at time 0 = $800
at time 1 = $800 x (3/4) x 1 = $600
at time 2 = $600 x 3/4 = $450
Value of the computer at time 3 = $450 x 3/4 = $337.50
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Reflect (0, -2) in the x-axis followed by the y-axis.
(0, -2) reflected in the x-axis followed by the y-axis is (,).
Therefore , the solution to the given problem of equation comes out to be The coordinates for the picture that is mirrored in the y-axis
are (-3, -2)
Define equationA formula for a mathematical equation combines two statements by using the equal sign (=) to denote equivalence. An equation in algebra is a statement proving the equality of two mathematical equations. For instance, the two numbers are connected by the equation 5x + 5 = 14. A mathematical relationship is built between the sentences on either side of a letter. Usually, the symbol serves as the only variable and the only factor. For instance, 8x - 4 = 2.
Here,
the specified point's coordinates are (3, -2).
Now,
(I) The image's coordinates that are reflected in the x-axis are (3, 2)
(ii) The coordinates for the picture that is mirrored in the y-axis are (-3, -2)
(iii) The point's coordinates for the x-axis reflection and the y-axis reflection will indeed be (-3, 2).
(iv) The point's coordinates that are reflected inside the source would be (-3, 2).
Therefore , the solution to the given problem of equation comes out to be The coordinates for the picture that is mirrored in the y-axis
are (-3, -2)
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If AD = 4 cm and AB = 6 cm, what is the perimeter of WXYZ?
Answer:
Step-by-step explanation:
no way to answer
Select all the equations that are equivalent to y - 4 = (x - 1).
It's important to note that equation y = x - 1 + 4 and y = x + 3 are in slope-intercept form, which is a common way to write linear equations.
How to determine the equivalent equation?
To determine if two equations are equivalent, you can check if they represent the same line in the cartesian plane. The following methods can be used to determine equivalent equations:
Graph the equations: You can graph the equations on the same coordinate plane and see if they produce the same line. If they do, the equations are equivalent.Check for the same slope and y-intercept: You can check if the equations have the same slope and y-intercept. If they do, the equations are equivalent.Solving for y: You can put the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, if the slope and y-intercept are the same for both equations, the equations are equivalent.The following equations are equivalent to y - 4 = (x - 1):
y = x - 1 + 4
y = x + 3
y - 4 = x - 1 + 4
y - 4 = x + 3 - 4
(y - 4) + 4 = (x - 1) + 4
y = x - 1 + 4
All of the above equations have the same slope and y-intercept, which means they represent the same line in the cartesian plane.
It's important to note that equation y = x - 1 + 4 and y = x + 3 are in slope-intercept form, which is a common way to write linear equations.
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2) A normal distribution has mean 700 and standard deviation 50. The probability is 0.6 that a randomly
selected term from this distribution is above x. What is x?
According to the normal distribution data given the value for x is obtained as 687.5.
What is normal distribution?
One of the families of continuous distributions, the standard normal distribution has a mean of zero and a standard deviation of one. Since most observations are grouped around the mean and mean=median=mode, the distribution is symmetric at the mean zero.
The value for mean is μ = 700.
The value for standard deviation is σ = 50.
The probability value is 0.6.
Use z score formula to solve for value of x -
P (X>x) = 0.6
0.6 = 1 - P (X>x)
0.4 = P[{(X-μ)/σ} ≤ {(x-700)/50}]
z0.4 = (x-700)/50
-0.25 = (x-700)/50
x = (-0.25 × 50) + 700
x = -12.5 + 700
x = 687.5
Therefore, the value for x is 687.5.
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help me its due today
Answer:
(1,-1)
Step-by-step explanation:
my guy, are you good? dude this question is so easy l m a o
anyways, heres the explanation
where there is an "x," replace it with a 1
so: -4-9y = 5
-9y = 9
y = -1
and the question already gives you what x is so:
(x,y)
(1,-1)
Solve for x round to the nearest tenth 33 27
What is an example of an acute triangle?
An acute triangle is a triangle with all three angles less than 90 degrees.
An example of an acute triangle is a triangle with angles measuring 30 degrees, 55 degrees, and 95 degrees. Using the Law of Cosines, we can calculate the side lengths of this triangle. The side opposite the 30 degree angle is 4.8, the side opposite the 55 degree angle is 5.2, and the side opposite the 95 degree angle is 8. The Law of Cosines states that the following equation must be true: a2 = b2 + c2 - 2bc Cos A. In this case, a2 = 82, b2 = 52, and c2 = 42. We can then solve for the sides of the triangle by plugging in the values for a2, b2, and c2 into the equation. The result is that the side lengths of this triangle are 4.8, 5.2, and 8.
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Triangle D has been dilated to create triangle D′. Use the image to answer the question.
Answer: It is C I got it right on the exam
Step-by-step explanation:
1. Which of the following is 60% in fraction form?A. 25B. 35C. 45
Answer:
I think 35
Step-by-step explanation:
Select the correct answer!!!
A club bought 6 equally priced pizzas and a large $15
bag of chips for a party. They spent a total of $ 69.
Write an equation modeling this, then solve.
I need an answer asappp
What is the exponential of 2?
Answer:
2^2 would be 4
Step-by-step explanation: