The radius of convergence R of the Taylor series is 2
The term convergence in math is defined as the process of a sequence or other function converging to a limit in a metric space.
Here we have know that the expression is written as,
=> f(x)=ln x, c=2.
By using the Taylor series formula we can write the expression like the following,
=> f(x) = ln(2) + ∑ (-1)ⁿ⁺¹ / n (2ⁿ)
Then the above power series will converge if and only if:
[tex]= > \lim_{n \to \infty} |\frac{-1}{(1+\frac{1}{n} )\times2}\times(x-2) | < 1[/tex]
When we simplify this one then we get,
=> |x-2/2| < 1
Then the value of x lies between 0 to 4.
And the Radius of convergent is 2.
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Find the area of the shaded region. Round your answer to the nearest hundredth.
Answer: Should be 6
Step-by-step explanation: 4 times for is 12
Then Make sure you divide 12 so u get 6.
A=1/2 BH
Jason paid $88.50 in tax on a table that cost $1,180. What was the tax rate?
If Jason paid $88.50 in tax on a table that cost $1,180, the tax rate (sales tax) is 7.5%.
What is the tax rate?The tax rate is the percentage that is paid in tax.
For sales tax (consumption tax), the tax rate is fixed, making it a proportional tax rate system.
For income tax, the tax rate follows a progressive tax rate system. The percentage of tax increases as the taxable income increases.
Some tax rates are said to be retrogressive as the rates reduce with increased taxable income.
The amount of sales tax on the table = $88.50
The cost of the table = $1,180
Tax rate = 7.5% ($88.50/$1,180 x 100)
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A lit of 5 poitive integer ha a mean, median, mode and range that are all 5. How many poible lit are there?
There is only 1 possible list of positive integers that have a mean, median, mode, and range of 5
As per the data given,
We have, a lit of 5 positive integers.
The sum of the five positive integers must equal five in order for the mean, median, mode, and range to all be five.
This is because the range of a set of equal numbers will always be 0, the mean of a set of equal numbers will always equal the numbers themselves, the median of a set of equal numbers will always equal the mean, the mode of a set of equal numbers will always equal the numbers themselves, and so on.
Therefore, there is only 1 possible list of positive integers that have a mean, median, mode, and range of 5: [5, 5, 5, 5, 5].
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Bonjour vous pouvez m’aider svp j'ai du mal.
Answer:
voir ci-dessous
Step-by-step explanation:
1.
Programme 1: choisi nombre par example, 2, prendre son carré, donc c'est 2²; ajourter5, donc c'est 4+5 =9
Programme 2: choisi nombre par example, 5, ajourter5, donc c'est 5+5 =10; prendre son carré, donc c'est 10²=100
2. f(x)=(x+5)² c'est programme 1; g(x)=x²+5 c'est programme 2
3. programme pour h(x) = (x+3)²:
choisir un nombreadjouter 3prendre son carrévoila.
Find the Volume.
Pls i need this answer its for a grade
64% as a fraction in simplest form and as a decimal 
Answer:
Step-by-step explanation:
64% as a fraction in its simplest form is 32/50.
As a decimal, 64% is equal to 0.64.
The top of the Points Bolivar Lighthouse in Port Bolivar, Texas, is 116 feet above sea level. The angle of depression from the light on the top of the tower to a passing ferry is 37°.
Which is closest to the distance in feet from the bottom of the lighthouse to the ferry?
133.3 ft
99.2 ft
153.9 ft
87.4 ft
The distance in feet from the bottom of the lighthouse to the ferry is 154 feet.
What is the angle of depression?
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.
The angle of depression is always measured from the horizontal.
A triangle is formed by the lighthouse, the ground, and the ferry. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the ferry. (Alternate angles on parallel lines)
The angle at the top of the lighthouse, inside the triangle is:
90° − 37° = 53°
The distance to the boat is the side opposite the angle of 63° while the height of the lighthouse is the adjacent side.
opposite / adjacent = tan53°
distance / 116 = tan53°
distance = 116 × tan53°
= 153.932 feet
= 153.9 feet. (approximately)
Hence, the distance in feet from the bottom of the lighthouse to the ferry is 153.9 feet.
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Given ST is tangent to circle Q, find the value of r
The value of the radius of the circle 'r' will be 14 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The tangent and radius of the circle intersect at the right angle. Then the value of 'r' is given as,
QT² = QS² + ST²
(r + 36)² = r² + 48²
r² + 72r + 1296 = r² + 2304
72r = 1008
r = 14
The value of the radius of the circle 'r' will be 14 units.
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Make and test a connector about the given quantity the product of any two even integers
The product of any two even integers is even.
What is even and odd number?Odd numbers: An odd number is any natural number that can be written as (2n + 1), where n is any natural number, i.e., a positive integer.
Even numbers: Any natural number that can be written as 2n, where n is any natural number, i.e., a positive integer, is referred to as an even number.
The product of two even numbers is even.
Let us suppose m and n be any integers.
So, 2m and 2k are two even numbers.
Take the product as 2m(2k) = 2(2mk), which is even.
Let the two even integers be x1 and x2.
Let x1 = 2
Let x2 = 6
Therefore, the product of x1 and x2 is
x1 * x2 = 2 * 6 = 12
The product is even since it is divisible by 2.
Hence, the product of any two even integers is even.
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Which function has a range of y greater-than-or-equal-to 0?
Step-by-step explanation: A square root function has a range of y greater-than-or-equal-to 0.
For example, the function f(x) = √x has a domain of x greater-than-or-equal-to 0 and a range of y greater-than-or-equal-to 0. This is because the square root of a positive number is always positive, and the square root of 0 is equal to 0. So, for any value of x greater-than-or-equal-to 0, the corresponding value of y will always be greater-than-or-equal-to 0.
Other functions that have a range of y greater-than-or-equal-to 0 include:
the absolute value function: f(x) = |x|
exponential functions with positive bases: f(x) = e^x, f(x) = 2^x, etc.
any linear function with a positive slope: f(x) = mx + b, where m > 0.
These are just a few examples of functions that have a range of y greater-than-or-equal-to 0.
twelve students took a placement exam with the following results. 90 64 99 71 72 93 40 85 45 50 55 66 what is the percentile rank of 64? round to the nearest percentile
The percentile rank of 64 in the twelve students exam result is 42%
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
Ordering the data we have:
90 64 99 71 72 93 40 85 45 50 55 66
40 > 45 > 50 > 55 > 64 > 66 > 71 > 72 > 85 > 90 > 93 > 99
The 64 result is the 5th term of all the results, so:
percentile rank = (term / total term) * 100%
percentile rank = 5/12 * 100%
percentile rank = 41.66%
41.66% round to the nearest percentile 42%
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10. DG, FG, and EG are perpendicular bisectors
Answer:
Step-by-step explanation:
A) To find the length of AD, we first find the length of the CD.
CD = (BE + EC)/2 = (3x + 12 + 6x - 9)/2 = 9x + 3
AD = CD = 9x + 3
B) To find x, we use the fact that DG is the perpendicular bisector of EC and BG. This means that EG = BG = x.
EG = BG = x
EC = 2EG = 2x
Substituting in EC = 6x - 9, we get:
2x = 6x - 9
4x = 9
x = 9/4 = 2.25
C) To find BC, we use the fact that BC = AB - 2BE
BC = AB - 2BE
BC = 10 - 2(3x + 12)
Substituting in x = 2.25, we get:
BC = 10 - 2(3 * 2.25 + 12)
BC = 10 - 2 * 21
BC = 10 - 42
BC = -32
Answer:
AD = 5, x = 7, BC = 66
Step-by-step explanation:
a) We know that DG is a perpendicular bisector, so it should divide AB into two equal parts, each equal to half the length of the total line segment.
So, AD = AB/2
= 10/2
= 5
b) Now, BE and EC are part of the same segment, as they share a common point E. Also, at E we have perpendicular bisector EG.
Again, the two parts BE and EC should be equal.
Given, BE = 3x + 12 and EC = 6x - 9
3x + 12 = 6x - 9
3x = 21
x = 7
c) Now, BC would be twice the length of one of the segments divided by the perpendicular bisector. So, BC = 2BE
= 2 * (3x + 12)
= 2 (3*7 + 12)
= 2 * 33
= 66
Damian dove into a wimming pool from that ide. He dove 5 feet down under the water. Then, He wam back to the urface. Write a integer (poitive or negative number) that repreent where he i now
Since Damian dove 5 feet under the water and then went back to the surface, he is now 0 feet below the surface. An integer that represents this is 0.
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z.
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction.
Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.
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What’s the length of ML?
The value of ML is 29.2.
Option B is the answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Two similar triangles:
So,
NL/RN = ML/QR
70/48 = ML/20
ML = (70 x 20) / 48
ML = 1400/48
ML = 29.2
Thus,
ML = 29.2
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What values complete each statement? Enter your answers in the boxes. (Square root 9)^2
Answer:
Step-by-step explanation:
( 9^2 ) = 23
find the distance between the plane 3z−(x 2y)=03z−(x 2y)=0 and the line ⟨3t−3,3t−1,3 3t⟩⟨3t−3,3t−1,3 3t⟩.
The distance between the plane 3z-(x,2y)=0 and the line ⟨3t-3,3t-1,3 3t⟩ is [tex]\frac{18}{\sqrt{14}}[/tex]
To find the distance between the plane 3z-(x,2y)=0 and the line ⟨3t-3,3t-1,3 3t⟩, we will use the formula for the distance between a point and a plane.
First, we find a point on the line by plugging in a value for t. Let's use t=1:
⟨3(1)-3,3(1)-1,3(3)(1)⟩ = ⟨0,-2,9⟩
Next, we find the normal vector for the plane:
n = (1,-2,3)
Finally, we can use the formula for the distance between a point and a plane:
d = |(⟨0,-2,9⟩-⟨0,0,0⟩)•n| ÷ ||n||
where ||n|| represents the magnitude of the normal vector n.
We calculate the dot product:
(⟨0,-2,9⟩-⟨0,0,0⟩)•n = ⟨0,-2,9⟩•(1,-2,3) = 0(-2) + (-2)(-2) + 9(3) = 18
And the magnitude of the normal vector:
||n|| [tex]= \sqrt{1^2 + (-2)^2 + 3^2} = \sqrt{1 + 4 + 9} = \sqrt{14}[/tex]
Putting it all together:
[tex]d = \frac{|18|}{\sqrt{14}} = \frac{18}{\sqrt{14}}[/tex]
So the distance between the plane 3z-(x,2y)=0 and the line ⟨3t-3,3t-1,3 3t⟩ is[tex]\frac{18}{\sqrt{14}}[/tex]
Correct Question:
Find the distance between the plane 3z−(x,2y)=0 and the line ⟨3t−3,3t−1,3 3t⟩⟨3t−3,3t−1,3 3t⟩.
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Please help, would like to know how to do it aswell as getting the answers
The measure of ∠FXD = 44°,
EG = 14 and ∠FZG = 21°.
What are triangles?A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is that the sum of its internal angles to 180 degrees. This quality is referred to as the angle sum property of triangles.
Given a triangle XYZ
and XG, YG, and ZG are angle bisectors,
DG = 14 and ZG = 17
∠DYE = 94°, ∠FXG = 22°
A: to find ∠FXD,
as we know angle bisector divides an angle into two equal parts,
so ∠FXG = ∠GXD = 22°
∠FXD = ∠FXG + ∠GXD
∠FXD = 22 + 22 = 44°
B: to find EG,
since G is the incenter,
Due to the junction point of the central axis being the center of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides.
so DG = EG = FG = 14
C: to find ∠FZG,
we have ∠DYE = 94° and ∠FXD = 44°
from angle sum property,
∠DYE + ∠FXD + ∠FZE = 180°
∠FZE + 94 + 44 = 180
∠FZE = 180 - 94 - 44
∠FZE = 42°
so ∠FZG = ∠GZE = ∠FZE/2 (due to angle bisector)
∠FZG = ∠GZE = 42/2
∠FZG = ∠GZE = 21°
Hence ∠FXD = 44°,
EG = 14,
∠FZG = 21°.
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Please help me on this the problem is the picture below
Answer:
WX
Step-by-step explanation:
WX is the only place where you can fold the triangle on that line and the 2 halves would fit perfectly over each other.
If the product of 485 x 35 is 16,975, what is the product of 485 x 3.5? How do you know?
Step-by-step explanation:
Without doing any math, 1,697.5
35.0 and 16,975 is the original
3.5 is 35.0, but they moved the decimal one point to the left
We do the same for the answer
16,975... we move the comma one point to the left and get 1,697.5
Concentric circles are internally tangent circles, true or false?
Concentric circles are internally tangent circles which is the true statement.
What is geometry?Geometry is the description of figures in a space with a specific number of dimensions and types. Plane geometry is the most prevalent sort of geometry (dealing with objects like the point, lines, circles, triangles, and polygons)
Concentric circles are circles that have the same center but different radii.
When two concentric circles are drawn, it is possible for them to be internally tangent, meaning that they touch each other at exactly one point and the point of tangency is inside both circles.
In this case, one circle is entirely contained within the other circle.
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12x squared minus 13x plus 3
Answer:
12x^2 - 13x + 3 is a quadratic equation in the standard form ax^2 + bx + c, where a = 12, b = -13, and c = 3. This equation can be factored, completed the square or used the quadratic formula to find the solutions of x.
5100 dollars is placed in an account with an annual interest rate of 7%. To the nearest year, how long will it take for the account value to reach 24000 dollars?
Please help me! I really need help:)
It will take approximately 20.7 years for the account value to reach $24000 with an annual interest rate of 7%. To the nearest year, it will take 21 years.
How to Determine the Time it Takes an Account Value to Reach a certain Amount?To find out how long it will take for an account with an initial value of $5100 to reach $24000 with an annual interest rate of 7%, you can use the formula:
time = (log(final value/initial value)) / (log(1+interest rate))
So, the time it will take for the account value to reach $24000 is:
time = (log(24000/5100)) / (log(1+0.07))
using the logarithm calculator or log rule
time = (log(4.64)) / (log(1.07))
time ≈ 20.7 years
To nearest year, it would take 21 years.
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if we exclude non-electrostatic forces, is it true to say that objects only attract each other if they have different charge? explain using observations made in this lab.
Yes, it is true to say that objects only attract each other if they have different charges if we exclude non-electrostatic forces.
This is because electrostatic forces between charged objects follow Coulomb's law, which states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. According to Coulomb's law, if two objects have the same charge, they will repel each other, while if they have different charges, they will attract each other.
This observation can be made in a lab by charging two objects with different charges (e.g. positive and negative) and observing their attraction towards each other, and then charging two objects with the same charge (e.g. both positive or both negative) and observing their repulsion from each other.
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2 (5V+ 7) > 10V +14
Answer:
This inequality has no solution.
Step-by-step explanation:
Solve the inequality.
Start on the left side.
Apply the distributive property.
[tex](2*5V)+(2*7) > 10V+14[/tex]
Simplify the parenthesis.
[tex]10V+14 > 10V+14[/tex]
Subtract [tex]10V[/tex] from both sides of the inequality.
[tex]14 > 14[/tex]
Since [tex]14 > 14[/tex], there are no solutions.
4] A ship sails 80 km on a bearing of 55° and then changes course and sails 40 km on
a bearing of 132° By making a scale diagram find: -
a) The final distance of the port from the ship.
b) The final bearing of the port from the ship.
Answer:
Below
Step-by-step explanation:
Break each of the legs into vertical and horizontal components so you can add them :
Vertical
80 sin 55 + 40 sin 132 = 95.258 km
Horizontal
80 cos 55 + 40 cos 132 = 19.121 km
Use pythag theorem to calculate the distance from origin
d^2 = 95.258^2 + 19.121^2
show d = 97.16 km from origin
Angle will be arctan ( 95.258/19.121) = 78.65° <====this is the bearing of the SHIP from the PORT....the bearing TO the PORT FROM the ship will be 78.165 + 180 = 258.65°
y-intercept of the line 17x–16y= – 20.
In Princeton's wig shop, 1/4 of the wigs are blonde and 2/3 of the wigs are brunette. What fraction of the wigs are either blonde or brunette?
Answer:
In Princeton's wig shop, the total number of wigs is the sum of the number of blonde wigs and the number of brunette wigs. Since 1/4 of the wigs are blonde and 2/3 of the wigs are brunette, the fraction of wigs that are either blonde or brunette is 7/12.
Answer:
[tex]\frac{11}{12}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}[/tex] + [tex]\frac{2}{3}[/tex] The common denominator is 12 make equivalent fractions with 12 as the denominator
[tex]\frac{1}{4}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{12}[/tex]
[tex]\frac{2}{3}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{8}{12}[/tex]
[tex]\frac{3}{12}[/tex] + [tex]\frac{8}{12}[/tex] = [tex]\frac{11}{12}[/tex]
Find 10·2 4/5 by using the Distributive Property.
Answer:
answer is 28
Step-by-step explanation:
10(2•4/5)
20 + 8
= 28
When you write it this way you distribute it so 10 is outside the parenthesis so you time 10 to bout of the numbers inside of it then add.
Antonia run a retaurant that ell two kind of deert. Antonia know the retaurant mut make at leat 18 and at mot 38 dozen of the Nutty Squirrel. The retaurant mut alo make between 9 and 20 dozen of the White Chocolate Blizzard. The dozen of Nutty Squirrel take 10 ounce of ugar, while dozen of White Chocolate Blizzard require 19 ounce of ugar. The retaurant only ha 570 ounce of ugar available. If dozen of Nutty Squirrel generate $9. 00 in income, and dozen of White Chocolate Blizzard generate $5. 00, how many dozen of the deert hould Antonia have the retaurant make to get the mot income?
Antonia should make 18 dozen of Nutty Squirrel and 20 dozen of White Chocolate Blizzard to get the most income, which would be $162.00.
Calculation the Most IncomeThe Nutty Squirrel requires 10 ounces of sugar per dozen, so Antonia can make at most 570 / 10 = 57 dozen of Nutty Squirrel.
Since Antonia has to make at least 18 dozen of Nutty Squirrel, she will make 18 dozen of Nutty Squirrel.
The White Chocolate Blizzard requires 19 ounces of sugar per dozen, so Antonia can make at most 570 / 19 = 30 dozen of White Chocolate Blizzard.
Since Antonia has to make between 9 and 20 dozen of White Chocolate Blizzard, she will make 20 dozen of White Chocolate Blizzard.
Therefore, Antonia should make 18 dozen of Nutty Squirrel and 20 dozen of White Chocolate Blizzard to get the most income, which would be 18 * $9.00 + 20 * $5.00 = $162.00.
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let y1, . . . , yn iid∼ f(y). find the sampling distribution of: y(1) = min i yi
A modified version of the original distribution, the sampling distributive of y(1) has an upper bound equal to the minimum value in the sample and a lower bound of 0.
Let y1,..., yn have an f-distribution and be independently and identically distributed (iid) (y).
Ascertain the y(1) = min I yi sampling distribution. The sampling distribution of y(1) has a lower bound of 0 and an upper bound that is equal to the minimum of the sample yi. It is a truncated distribution of the original distribution f(y).
By integrating the initial distribution f(y) from 0 to the minimum of the sample yi, get the probability of each value of y(1).
A reduced version of the original distribution f(y), with a lower bound of 0 and an upper bound equal to the minimum of the sample yi, is the sampling distribution of y(1). We must integrate the initial distribution f in order to calculate this distribution (y)
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